Existence of solutions for second-order integral boundary value problems

In this paper, using a new comparison result and monotone iterative method, we consider the existence of solution of integral boundary value problem for second-order differential equation. To obtain corresponding results, we also discuss second order differential inequalities. The interesting point is that the one-sided Lipschitz constant is related to the first eigenvalues corresponding to the relevant operators.

[1]  Gennaro Infante,et al.  Positive Solutions of Nonlocal Boundary Value Problems: A Unified Approach , 2006 .

[2]  Zhongli Wei,et al.  Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative , 2010 .

[3]  Zhilin Yang,et al.  Existence and nonexistence results for positive solutions of an integral boundary value problem , 2006 .

[4]  W. M. Whyburn.  Differential equations with general boundary conditions , 1942 .

[5]  Xingqiu Zhang,et al.  On multiple sign-changing solutions for some second-order integral boundary value problems , 2010 .

[6]  J. Webb,et al.  Positive solutions of nonlocal boundary value problems involving integral conditions , 2008 .

[7]  Juan J. Nieto,et al.  Monotone method for first-order functional differential equations , 2006, Comput. Math. Appl..

[8]  Solvability and positive solution of a system of second-order boundary value problem with integral boundary conditions , 2014 .

[9]  Gennaro Infante,et al.  Existence and localization of positive solutions for a nonlocal BVP arising in chemical reactor theory , 2014, Commun. Nonlinear Sci. Numer. Simul..

[10]  Juan J. Nieto,et al.  An abstract monotone iterative technique , 1997 .

[11]  Artūras Štikonas,et al.  A survey on stationary problems, Green’s functions and spectrum of Sturm–Liouville problem with nonlocal boundary conditions , 2014 .

[12]  Weigao Ge,et al.  Existence result of second-order differential equations with integral boundary conditions at resonance , 2009 .

[13]  J. Mawhin,et al.  Maximum Principles Around An Eigenvalue With Constant Eigenfunctions , 2008 .

[14]  A. Štikonas.  Investigation of Characteristic Curve for Sturm–Liouville Problem with Nonlocal Boundary Conditions on Torus , 2011 .

[15]  Alberto Cabada,et al.  An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions , 2011 .

[16]  Existence of solutions to functional boundary value problem of second-order nonlinear differential equation , 2011 .

[17]  Patrick Habets,et al.  Two-Point Boundary Value Problems: Lower and Upper Solutions , 2012 .

[18]  Zhilin Yang.  Existence and uniqueness of positive solutions for an integral boundary value problem , 2008 .

[19]  Juan J. Nieto,et al.  Second-Order Boundary Value Problem with Integral Boundary Conditions , 2011 .

[20]  Jingxian Sun,et al.  On existence of positive solutions of coupled integral boundary value problems for a nonlinear singular superlinear differential system , 2012 .

[21]  Yumei Zou,et al.  Monotone iterative method for differential systems with coupled integral boundary value problems , 2013 .

[22]  Alberto Cabada,et al.  Existence results for nonlinear problems with separated boundary conditions , 1999 .

[23]  J. Webb,et al.  Existence of positive solutions for a thermostat model , 2012 .

[24]  Shuqin Zhang,et al.  Monotone iterative method for initial value problem involving Riemann–Liouville fractional derivatives , 2009 .

[25]  Gennaro Infante,et al.  NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS , 2006, Proceedings of the Edinburgh Mathematical Society.