Chapter 1 Progress in Nonlinear Differential Equations(1) 1.1 p-Laplacian type equations(1) 1.2 Prescribed mean curvature equations(2) 1.3 Impulsive differential equations(4) 1.4 Functional differential equations(5) 1.5 Fractional differential equations(7) 1.6 Elastic beam equations(10) References(11) Chapter 2 Basic Definitions and Theorems(16) 2.1 Cone and Fixed point theorems(16) 2.2 Coincidence degree theory(19) 2.3 Fractional calculus(19) 2.4 H¨older’s Inequality(21) 2.5 Time-map Analysis and Bifurcation Diagrams(21) References(22) Chapter 3 p-Laplacian type equations(24) 3.1 Exact number of solutions for a class of two-point boundary value problems with one-dimensional p-Laplacian(24) 3.2 Exact number of pseudo-symmetric positive solutions for a p-Laplacian three-point boundary value problems(33) 3.3 Existence of a positive solution for one-dimensional singular p-Laplacian problems and its parameter dependence(42) 3.4 Notes and comments(59) References(59) Chapter 4 Prescribed Mean Curvature Operator Equations(61) 4.1 Exact multiplicity and bifurcation diagrams of positive solutions of a one-dimensional prescribed mean curvature equation with concave-convex nonlinearities(61) 4.2 Time map analysis to establish the exact number of positive solutions of one-dimensional prescribed mean curvature equations(72) 4.3 Periodic solutions for prescribed mean curvature Li′enard equation with a deviating argument(88) 4.4 Notes and comments(94) References(95) Chapter 5 Green’s Function and Fractional Differential Equations(96) 5.1 The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions(96) 5.2 New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions(105) 5.3 Green’s function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application(118) 5.4 Notes and comments(134) References(135) Chapter 6 Elasticity Beam Equations(136) 6.1 Symmetric positive solutions of elasticity beam equations with integral boundary conditions(136) 6.2 New existence theory of positive solutions to fourth order p-Laplacian elasticity problems(150) 6.3 Multiple positive solutions of fourth order impulsive differential equations with integral boundary conditions and one-dimensional p-Laplacian(168) 6.4 Notes and comments(185) References(185) Chapter 7 Functional Differential Equations(187) 7.1 Existence, multiplicity, and dependence on a parameter for a functional differential equation(188) 7.2 Positive periodic solutions of first-order impulsive functional differential equations(197) 7.3 Periodic solution and nontrivial periodic solutions for a class of Rayleigh type equation with two deviating arguments(213) 7.4 Anti-periodic solutions to Rayleigh-type equations with two deviating arguments(222) 7.5 Positive solutions for a second-order singular differential equations with a delayed argument(227) 7.6 Positive solutions for second order impulsive p-Laplacian equations with deviating arguments(237) 7.7 Notes and comments(255) References(256) Chapter 8 Nonlinear Impulsive Differential Equations(258) 8.1 Parameter dependence of positive solutions for second order singular impulsive differential equations(259) 8.2 Impulsive differential equations of one-dimensional singular p-Laplacian with two parameters(265) 8.3 Multi-parameter fourth order impulsive differential equations with one-dimensional m-Laplacian and deviating arguments(281) 8.4 Transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations(299) 8.5 Transformation technique and positive solutions for second-order impulsive differential equations with deviating arguments(312) 8.6 Notes and comments(323) References(324) Index(326)
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