Professor Jeffrey Webb
- Honorary Senior Research Fellow (School of Mathematics & Statistics)
Publications
2024
Webb, J. R. L. and Lan, Kunquan (2024) Fractional differential equations of Bagley-Torvik and Langevin type. Fractional Calculus and Applied Analysis, (doi: 10.1007/s13540-024-00292-2) (Early Online Publication)
2023
Lan, Kunquan and Webb, J.R.L. (2023) A new Bihari inequality and initial value problems of first order fractional differential equations. Fractional Calculus and Applied Analysis, 26(3), pp. 962-988. (doi: 10.1007/s13540-023-00152-5)
2022
Webb, Jeffrey R.L. (2022) Compactness of nonlinear integral operators with discontinuous and with singular kernels. Journal of Mathematical Analysis and Applications, 509(2), 126000. (doi: 10.1016/j.jmaa.2022.126000)
2017
Webb, J.R.L. (2017) New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, 49(3), pp. 534-547. (doi: 10.1112/blms.12055)
2012
Webb, J.R.L. (2012) Existence of positive solutions for a thermostat model. Nonlinear Analysis: Real World Applications, 13(2), pp. 923-938. (doi: 10.1016/j.nonrwa.2011.08.027)
2011
Webb, J. (2011) Positive solutions of a boundary value problem with integral boundary conditions. Electronic Journal of Differential Equations, 55, pp. 1-10.
2010
Webb, J.R.L. (2010) Remarks on a non-local boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 72(2), pp. 1075-1077. (doi: 10.1016/j.na.2009.07.047)
Webb, J.R.L. (2010) Remarks on nonlocal boundary value problems at resonance. Applied Mathematics and Computation, 216(2), pp. 497-500. (doi: 10.1016/j.amc.2010.01.056)
Webb, J.R.L. (2010) Solutions of nonlinear equations in cones and positive linear operators. Journal of the London Mathematical Society, 82(2), pp. 420-436. (doi: 10.1112/jlms/jdq037)
Webb, J.R.L. (2010) Positive solutions of some higher order nonlocal boundary value problems. Electronic Journal of Qualitative Theory of Differential Equations, Spec.(29), pp. 1-15.
2009
Graef, J.R. and Webb, J.R.L. (2009) Third order boundary value problems with nonlocal boundary conditions. Nonlinear Analysis, 71(5-6), pp. 1542-1551. (doi: 10.1016/j.na.2008.12.047)
Webb, J.R.L. (2009) Non-local conjugate type boundary value problems of higher order. Nonlinear Analysis, 71(5-6), pp. 1933-1940. (doi: 10.1016/j.na.2009.01.033)
Webb, J.R.L. and Zima, M. (2009) Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems. Nonlinear Analysis: Theory, Methods and Applications, 71(3-4), pp. 1369-1378. (doi: 10.1016/j.na.2008.12.010)
Webb, J.R.L. (2009) Remarks on u 0-positive operators. Journal of Fixed Point Theory and Applications, 5(1), pp. 37-45. (doi: 10.1007/s11784-008-0093-2)
Webb, J.R.L. and Infante, G. (2009) Nonlocal boundary value problems of arbitrary order. Journal of the London Mathematical Society, 79(1), pp. 238-258. (doi: 10.1112/jlms/jdn066)
Webb, J.R.L. (2009) Higher order non-local (n-1, 1) conjugate type boundary value problems. In: Cabada, A., Liz, E. and Nieto, J.J. (eds.) Mathematical Models In Engineering, Biology And Medicine. Series: AIP Conference Proceedings (1124). American Institute of Physics: Melville, NY, pp. 332-341. ISBN 978-0-7354-0660-5
Webb, J.R.L. and Infante, G. (2009) Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure and Applied Analysis, 9(2), pp. 563-581. (doi: 10.3934/cpaa.2010.9.563)
Webb, J.R.L. (2009) Boundary value problems with vanishing Green's function. Communications in Applied Analysis, 13,
2008
Webb, J.R.L., Infante, G. and Franco, D. (2008) Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 138(2), pp. 427-446. (doi: 10.1017/S0308210506001041)
Webb, J.R.L. (2008) Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems: Series S, 1(1), pp. 177-186. (doi: 10.3934/dcdss.2008.1.177)
Webb, J.R.L. and Infante, G. (2008) Positive solutions of nonlocal boundary value problems involving integral conditions. No DEA - Nonlinear Differential Equations and Applications, 15(1-2), pp. 45-67. (doi: 10.1007/s00030-007-4067-7)
2007
Khan, R.A. and Webb, J.R.L. (2007) Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth. Journal of Mathematical Analysis and Applications, 328(1), pp. 690-698. (doi: 10.1016/j.jmaa.2006.05.074)
2006
Webb, J.R.L. and Infante, G. (2006) Positive solutions of nonlocal boundary value problems: a unified approach. Journal of the London Mathematical Society, 74(3), pp. 673-693. (doi: 10.1112/S0024610706023179)
Infante, G. and Webb, J.R.L. (2006) Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations. Proceedings of the Edinburgh Mathematical Society, 49(3), pp. 637-656. (doi: 10.1017/S0013091505000532)
Franco, D. and Webb, J.R.L. (2006) Collisionless orbits of singular and non singular dynamical systems. Discrete and Continuous Dynamical Systems: Series A, 15(3), pp. 747-757. (doi: 10.3934/dcds.2006.15.747)
Infante, G. and Webb, J.R.L. (2006) Loss of positivity in a nonlinear scalar heat equation. Nonlinear Differential Equations and Applications, 13(2), pp. 249-261. (doi: 10.1007/s00030-005-0039-y)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least three solutions of a second-order three-point boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 64(6), pp. 1356-1366. (doi: 10.1016/j.na.2005.06.040)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least two solutions of second order nonlinear three point boundary value problems. Dynamic Systems and Applications, 15, pp. 119-132.
Webb, JRL and Lan, KQ (2006) Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topological Methods in Nonlinear Analysis, 27, pp. 91-115.
2005
Guo, Z.M. and Webb, J.R.L. (2005) Structure of boundary blow-up solutions for quasilinear elliptic problems I. Large and small solutions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 135, pp. 615-642.
Guo, ZM and Webb, JRL (2005) Structure of boundary blow-up solutions for quasi-linear elliptic problems II: small and intermediate solutions. Journal of Differential Equations, 211, pp. 187-217. (doi: 10.1016/j.jde.2004.06.008)
Webb, J.R.L. (2005) Multiple positive solutions of some nonlinear heat flow problems. Discrete and Continuous Dynamical Systems, Suppl., pp. 895-903.
Webb, JRL (2005) Optimal constants in a nonlocal boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 63, pp. 672-685. (doi: 10.1016/j.na.2005.02.055)
2003
Guo, ZM and Webb, JRL (2003) Profile of solutions with sharp layers to some singularly perturbed quasilinear Dirichlet problems. Communications in Contemporary Mathematics, 5, pp. 883-920.
Infante, G. and Webb, J. (2003) Positive solutions of some nonlocal boundary value problems. Abstract and Applied Analysis(18), pp. 1047-1060. (doi: 10.1155/S1085337503301034)
Webb, J.R.L. (2003) Extensions of Gronwall's inequality with logarithmic terms. In: Barletta, E. (ed.) Lecture notes of Seminario Interdisciplinare di Matematica. Dipartimento di Matematica, Universita degli Studi della Basilicata: Potenza, pp. 149-159.
Webb, J.R.L. (2003) Three-point boundary value problems with solutions that change sign. Journal of Integral Equations and Applications, 15(1), pp. 37-57. (doi: 10.1216/jiea/1181074944)
2002
Guo, ZM and Webb, JRL (2002) Large and small solutions of a class of quasilinear elliptic eigenvalue problems. Journal of Differential Equations, 180, pp. 1-50. (doi: 10.1006/jdeq.2001.4049)
Infante, G and Webb, JRL (2002) A finite dimensional approach to nonlinear spectral theory. Nonlinear Analysis: Theory, Methods and Applications, 51, pp. 171-188.
Infante, G and Webb, JRL (2002) Nonzero solutions of Hammerstein integral equations with discontinuous kernels. Journal of Mathematical Analysis and Applications, 272, pp. 30-42.
Lan, KQ and Webb, JRL (2002) A-properness of contractive and condensing maps. Nonlinear Analysis: Theory, Methods and Applications, 49, pp. 885-895.
Webb, J.R.L. (2002) Remarks on positive solutions of some three point boundary value problems. In: Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, 24-27 May, 2002, pp. 905-915.
2001
Webb, JRL (2001) Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods and Applications, 47, pp. 4319-4332.
Articles
Webb, J. R. L. and Lan, Kunquan (2024) Fractional differential equations of Bagley-Torvik and Langevin type. Fractional Calculus and Applied Analysis, (doi: 10.1007/s13540-024-00292-2) (Early Online Publication)
Lan, Kunquan and Webb, J.R.L. (2023) A new Bihari inequality and initial value problems of first order fractional differential equations. Fractional Calculus and Applied Analysis, 26(3), pp. 962-988. (doi: 10.1007/s13540-023-00152-5)
Webb, Jeffrey R.L. (2022) Compactness of nonlinear integral operators with discontinuous and with singular kernels. Journal of Mathematical Analysis and Applications, 509(2), 126000. (doi: 10.1016/j.jmaa.2022.126000)
Webb, J.R.L. (2017) New fixed point index results and nonlinear boundary value problems. Bulletin of the London Mathematical Society, 49(3), pp. 534-547. (doi: 10.1112/blms.12055)
Webb, J.R.L. (2012) Existence of positive solutions for a thermostat model. Nonlinear Analysis: Real World Applications, 13(2), pp. 923-938. (doi: 10.1016/j.nonrwa.2011.08.027)
Webb, J. (2011) Positive solutions of a boundary value problem with integral boundary conditions. Electronic Journal of Differential Equations, 55, pp. 1-10.
Webb, J.R.L. (2010) Remarks on a non-local boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 72(2), pp. 1075-1077. (doi: 10.1016/j.na.2009.07.047)
Webb, J.R.L. (2010) Remarks on nonlocal boundary value problems at resonance. Applied Mathematics and Computation, 216(2), pp. 497-500. (doi: 10.1016/j.amc.2010.01.056)
Webb, J.R.L. (2010) Solutions of nonlinear equations in cones and positive linear operators. Journal of the London Mathematical Society, 82(2), pp. 420-436. (doi: 10.1112/jlms/jdq037)
Webb, J.R.L. (2010) Positive solutions of some higher order nonlocal boundary value problems. Electronic Journal of Qualitative Theory of Differential Equations, Spec.(29), pp. 1-15.
Graef, J.R. and Webb, J.R.L. (2009) Third order boundary value problems with nonlocal boundary conditions. Nonlinear Analysis, 71(5-6), pp. 1542-1551. (doi: 10.1016/j.na.2008.12.047)
Webb, J.R.L. (2009) Non-local conjugate type boundary value problems of higher order. Nonlinear Analysis, 71(5-6), pp. 1933-1940. (doi: 10.1016/j.na.2009.01.033)
Webb, J.R.L. and Zima, M. (2009) Multiple positive solutions of resonant and non-resonant nonlocal boundary value problems. Nonlinear Analysis: Theory, Methods and Applications, 71(3-4), pp. 1369-1378. (doi: 10.1016/j.na.2008.12.010)
Webb, J.R.L. (2009) Remarks on u 0-positive operators. Journal of Fixed Point Theory and Applications, 5(1), pp. 37-45. (doi: 10.1007/s11784-008-0093-2)
Webb, J.R.L. and Infante, G. (2009) Nonlocal boundary value problems of arbitrary order. Journal of the London Mathematical Society, 79(1), pp. 238-258. (doi: 10.1112/jlms/jdn066)
Webb, J.R.L. and Infante, G. (2009) Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure and Applied Analysis, 9(2), pp. 563-581. (doi: 10.3934/cpaa.2010.9.563)
Webb, J.R.L. (2009) Boundary value problems with vanishing Green's function. Communications in Applied Analysis, 13,
Webb, J.R.L., Infante, G. and Franco, D. (2008) Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 138(2), pp. 427-446. (doi: 10.1017/S0308210506001041)
Webb, J.R.L. (2008) Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete and Continuous Dynamical Systems: Series S, 1(1), pp. 177-186. (doi: 10.3934/dcdss.2008.1.177)
Webb, J.R.L. and Infante, G. (2008) Positive solutions of nonlocal boundary value problems involving integral conditions. No DEA - Nonlinear Differential Equations and Applications, 15(1-2), pp. 45-67. (doi: 10.1007/s00030-007-4067-7)
Khan, R.A. and Webb, J.R.L. (2007) Existence of at least three solutions of nonlinear three point boundary value problems with super-quadratic growth. Journal of Mathematical Analysis and Applications, 328(1), pp. 690-698. (doi: 10.1016/j.jmaa.2006.05.074)
Webb, J.R.L. and Infante, G. (2006) Positive solutions of nonlocal boundary value problems: a unified approach. Journal of the London Mathematical Society, 74(3), pp. 673-693. (doi: 10.1112/S0024610706023179)
Infante, G. and Webb, J.R.L. (2006) Nonlinear non-local boundary-value problems and perturbed Hammerstein integral equations. Proceedings of the Edinburgh Mathematical Society, 49(3), pp. 637-656. (doi: 10.1017/S0013091505000532)
Franco, D. and Webb, J.R.L. (2006) Collisionless orbits of singular and non singular dynamical systems. Discrete and Continuous Dynamical Systems: Series A, 15(3), pp. 747-757. (doi: 10.3934/dcds.2006.15.747)
Infante, G. and Webb, J.R.L. (2006) Loss of positivity in a nonlinear scalar heat equation. Nonlinear Differential Equations and Applications, 13(2), pp. 249-261. (doi: 10.1007/s00030-005-0039-y)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least three solutions of a second-order three-point boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 64(6), pp. 1356-1366. (doi: 10.1016/j.na.2005.06.040)
Khan, R.A. and Webb, J.R.L. (2006) Existence of at least two solutions of second order nonlinear three point boundary value problems. Dynamic Systems and Applications, 15, pp. 119-132.
Webb, JRL and Lan, KQ (2006) Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type. Topological Methods in Nonlinear Analysis, 27, pp. 91-115.
Guo, Z.M. and Webb, J.R.L. (2005) Structure of boundary blow-up solutions for quasilinear elliptic problems I. Large and small solutions. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 135, pp. 615-642.
Guo, ZM and Webb, JRL (2005) Structure of boundary blow-up solutions for quasi-linear elliptic problems II: small and intermediate solutions. Journal of Differential Equations, 211, pp. 187-217. (doi: 10.1016/j.jde.2004.06.008)
Webb, J.R.L. (2005) Multiple positive solutions of some nonlinear heat flow problems. Discrete and Continuous Dynamical Systems, Suppl., pp. 895-903.
Webb, JRL (2005) Optimal constants in a nonlocal boundary value problem. Nonlinear Analysis: Theory, Methods and Applications, 63, pp. 672-685. (doi: 10.1016/j.na.2005.02.055)
Guo, ZM and Webb, JRL (2003) Profile of solutions with sharp layers to some singularly perturbed quasilinear Dirichlet problems. Communications in Contemporary Mathematics, 5, pp. 883-920.
Infante, G. and Webb, J. (2003) Positive solutions of some nonlocal boundary value problems. Abstract and Applied Analysis(18), pp. 1047-1060. (doi: 10.1155/S1085337503301034)
Webb, J.R.L. (2003) Three-point boundary value problems with solutions that change sign. Journal of Integral Equations and Applications, 15(1), pp. 37-57. (doi: 10.1216/jiea/1181074944)
Guo, ZM and Webb, JRL (2002) Large and small solutions of a class of quasilinear elliptic eigenvalue problems. Journal of Differential Equations, 180, pp. 1-50. (doi: 10.1006/jdeq.2001.4049)
Infante, G and Webb, JRL (2002) A finite dimensional approach to nonlinear spectral theory. Nonlinear Analysis: Theory, Methods and Applications, 51, pp. 171-188.
Infante, G and Webb, JRL (2002) Nonzero solutions of Hammerstein integral equations with discontinuous kernels. Journal of Mathematical Analysis and Applications, 272, pp. 30-42.
Lan, KQ and Webb, JRL (2002) A-properness of contractive and condensing maps. Nonlinear Analysis: Theory, Methods and Applications, 49, pp. 885-895.
Webb, JRL (2001) Positive solutions of some three point boundary value problems via fixed point index theory. Nonlinear Analysis: Theory, Methods and Applications, 47, pp. 4319-4332.
Book Sections
Webb, J.R.L. (2009) Higher order non-local (n-1, 1) conjugate type boundary value problems. In: Cabada, A., Liz, E. and Nieto, J.J. (eds.) Mathematical Models In Engineering, Biology And Medicine. Series: AIP Conference Proceedings (1124). American Institute of Physics: Melville, NY, pp. 332-341. ISBN 978-0-7354-0660-5
Webb, J.R.L. (2003) Extensions of Gronwall's inequality with logarithmic terms. In: Barletta, E. (ed.) Lecture notes of Seminario Interdisciplinare di Matematica. Dipartimento di Matematica, Universita degli Studi della Basilicata: Potenza, pp. 149-159.
Conference Proceedings
Webb, J.R.L. (2002) Remarks on positive solutions of some three point boundary value problems. In: Fourth International Conference on Dynamical Systems and Differential Equations, Wilmington, NC, 24-27 May, 2002, pp. 905-915.