Fourth order elliptic boundary value problem with nonlinear term decaying at the origin

Tacksun Jung,Q-Heung Choi

doi:10.1186/1029-242x-2013-432

Abstract

We consider the number of the weak solutions for some fourth order elliptic boundary value problem with bounded nonlinear term decaying at the origin. We get a theorem, which shows the existence of the bounded solution for this problem. We obtain this result by approaching the variational method and using the generalized mountain pass theorem for the fourth order elliptic problem with bounded nonlinear term.MSC:35J30, 35J40.

Highlights

Let be a bounded domain in Rn with smooth boundary ∂
We consider the number of the weak solutions for the following fourth order elliptic problem with the Dirichlet boundary condition
We assume that g ∈ C ( × R, R) satisfies the following: (g ) g ∈ C ( × R, R), (g ) g(x, ) =, g(x, ξ ) = o(|ξ |) uniformly with respect to x ∈, (g ) there exists C > such that |g(x, ξ )| < C ∀(x, ξ ) ∈ × R

Summary

Introduction

Let be a bounded domain in Rn with smooth boundary ∂. We consider the number of the weak solutions for the following fourth order elliptic problem with the Dirichlet boundary condition ) to the problem with bounded nonlinear term and applying the maximum principle for the elliptic operator – and – – c two times and the mountain pass theorem in the critical point theory.

Results

Conclusion