Existence of symmetric solutions for a class of BVP with integral boundary conditions

Abstract

In this paper, we study the symmetric solutions of second-order BVP with integral boundary conditions. By using a generalized Leggett-Williams fixed point theorem and some other techniques, we obtain sufficient conditions for the existence of symmetric positive solutions for the system. Meanwhile, an example is devoted to demonstrate our results in the end.

A family of singular ordinary differential equations of the third order with an integral boundary condition

“…There are results on the existence and asymptotic estimates of solutions for third order ordinary differential equations with singularly perturbed boundary value problems, which depend on a small positive parameter see for example [16,19,27], on third order ordinary differential equations with singularly perturbed boundary value problems and with nonlinear coefficients or boundary conditions see for example [3,12,29,50], on third order ordinary differential equations with nonlinear boundary value problems see for example [18,28], on existence results for third order ordinary differential equations see for example [17,24], and particularly third order ordinary differential equations with integral boundary conditions see for example [2,6,7,20,21,39,42,47,49] In the last years there are several papers which consider integral or nonlocal boundary conditions on different branches of applications, e.g. for the heat equations see for example [10,13,14,15,22,26,30,34,35,36,38], for the wave equations [37], for the second order ordinary differential equations see for example [5,31,33,44,52,53,54], for the fourth order ordinary differential equations see for example…”

“…In the last years there have been published several papers which consider integral or nonlocal boundary conditions on different branches of applications, e.g., for the heat equations, see for example [22][23][24][25][26][27][28][29][30][31][32], for the wave equations [33], for the second order ordinary differential equations, see for example [34][35][36][37][38][39][40], for the fourth order ordinary differential equations, see for example [41,42], for higher order ordinary differential equations, see for example [43], for fractional differential equations, see for example [44][45][46].…”