Multiple positive solutions for discrete nonlocal boundary value problems

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 Some Higher Order Nonlocal Boundary Value Problems

We show how a unified method, due to Webb and Infante, of tackling many nonlocal boundary value problems, can be applied to nonlocal versions of some recently studied higher order boundary value problems. In particular, we give some explicit examples and calculate the constants that are required by the theory.

Positive Solutions of Some Nonlocal Boundary Value Problems

Positive Solutions and Eigenvalues of Nonlocal Boundary-value Problems

We study the ordinary differential equation x′′ + λa(t)f(x) = 0 with the boundary conditions x(0) = 0 and x′(1) = R 1 η x ′(s)dg(s). We characterize values of λ for which boundary-value problem has a positive solution. Also we find appropriate intervals for λ so that there are two positive solutions.