A multiplicity result for p-Lapacian boundary value problems via critical points theorem

摘要

In this paper, we deal with the existence of at least three classical solutions for the following two point boundary value problem {(phi(p)(u '))' + lambda f(t,u) = 0, alpha(1)u(a) - alpha(2)u '(a) = 0, beta(1)u(b) + beta(2)u '(b) = 0, where phi(p) (s) = |s|(p-2)s, p > 1 is a constant, lambda is a positive parameter, a, b epsilon R, a < b. Our main tool is a recent three critical point theorem of Ricceri. Our emphasis here is constructing an appropriate separable and reflexive real Banach space. (C) 2008 Elsevier Inc. All rights reserved.