Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems

Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Positive solutions of discrete Neumann boundary value problems with sign-changing nonlinearities

R + →R is a sign-changing function. In recent years, positive solutions of boundary value problems for difference equations have been widely studied. See [–] and the references therein. However, little work has been done that has referred to the existence of positive solutions for discrete boundary value problems with sign-changing nonlinearities (see []). Usually, in order to obtain posit...

Existence of non-spurious solutions to discrete boundary value problems

This paper investigates discrete boundary value problems (BVPs) involving secondorder difference equations and two-point boundary conditions. General theorems guaranteeing the existence and uniqueness of solutions to the discrete BVP are established. The methods involve a sufficient growth condition to yield an a priori bound on solutions to a certain family of discrete BVPs. The a priori bound...

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.