Sign-Changing and Extremal Constant-Sign Solutions of Nonlinear Elliptic Neumann Boundary Value Problems

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...

Infinitely Many Solutions for Elliptic Boundary Value Problems with Sign-changing Potential

In this article, we study the elliptic boundary value problem −∆u + a(x)u = g(x, u) in Ω,

Multiple Positive Solutions for Nonlinear Second-order M-point Boundary-value Problems with Sign Changing Nonlinearities

In this paper, we study the nonlinear second-order m-point boundary value problem u′′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, βu(0)− γu′(0) = 0, u(1) = m−2 X i=1 αiu(ξi), where the nonlinear term f is allowed to change sign. We impose growth conditions on f which yield the existence of at least two positive solutions by using a fixed-point theorem in double cones. Moreover, the associated Green’s function...

A Minmax Principle, Index of the Critical Point, and Existence of Sign Changing Solutions to Elliptic Boundary Value Problems

In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems. We prove that, when isolated, the local degree of any solution given by this minmax principle is +1. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is a...

On the Morse Indices of Sign Changing Solutions of Nonlinear Elliptic Problems