Báo Cáo Báo cáo hóa học EXISTENCE OF INFINITELY MANY NODAL SOLUTIONS FOR A SUPERLINEAR NEUMANN BOUNDARY VALU

EXISTENCE OF INFINITELY MANY NODAL SOLUTIONS FOR A SUPERLINEAR NEUMANN BOUNDARY VALUE PROBLEM AIXIA QIAN Received 12 January 2005 We study the existence of a class of nonlinear elliptic equation with Neumann boundary condition, and obtain infinitely many nodal solutions. The study of such a problem is based on the variational methods and critical point theory. We prove the conclusion by using the symmetric mountain-pass theorem under the Cerami condition.


1. Introduction Consider the Neumann boundary value problem: ư u + αu = f (x,u), ∂u = 0, ∂ν x ∈ Ω, (1.1) x ∈ ∂Ω, where Ω ⊂ RN (N ≥ 1) is a bounded domain with smooth boundary ∂Ω and α 0 is a constant. Denote by σ(ư ) := {λi | 0 = λ1