Spectrum of Discrete Second-Order Neumann Boundary Value Problems with Sign-Changing Weight

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...

Sign-Changing Solutions for Discrete Second-Order Three-Point Boundary Value Problems

Positive solutions of second-order m-point boundary value problems with changing sign singular nonlinearity

In this work, some new existence results of positive solutions for a class of singular m-point boundary value problems with changing sign nonlinearity are obtained, which improve on many known results. c © 2006 Elsevier Ltd. All rights reserved.

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

In this article, we study the second-order three-point boundaryvalue problem u′′(t) + a(t)u′(t) + f(t, u) = 0, 0 ≤ t ≤ 1, u′(0) = 0, u(1) = αu(η), where 0 < α, η < 1, a ∈ C([0, 1], (−∞, 0)) and f is allowed to change sign. We show that there exist two positive solutions by using Leggett-Williams fixed-point theorem.

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...