Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
843389 | Nonlinear Analysis: Theory, Methods & Applications | 2008 | 13 Pages |
Abstract
In this paper we deal with the existence of weak solutions for quasilinear elliptic problem involving a pp-Laplacian of the form {−Δpu+λ(x)|u|p−2u=f(x,u)in Ω,|∇u|p−2∂u∂ν=η|u|p−2uon ∂Ω. We consider the above problem under several conditions on ff. For ff “superlinear” and subcritical with respect to uu, we prove the existence of infinitely many solutions of the above problem by using the “fountain theorem” and the “dual fountain theorem” respectively. For the case where ff is critical with a subcritical perturbation, namely f(x,u)=|u|p∗−2u+|u|r−2uf(x,u)=|u|p∗−2u+|u|r−2u, we show that there exists at least a nontrivial solution when p
Keywords
Related Topics
Physical Sciences and Engineering
Engineering
Engineering (General)
Authors
Ji-Hong Zhao, Pei-Hao Zhao,