Sign-variations of solutions of nonlinear discrete boundary value problems

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Multiple solutions for discrete boundary value problems

A recent multiplicity theorem for the critical points of a functional defined on a finite– dimensional Hilbert space, established by Ricceri, is extended. An application to Dirichlet boundary value problems for difference equations involving the discrete p–Laplacian operator is presented. Mathematics Subject Classification (2000): 39A10, 47J30.

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.

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