Article ID Journal Published Year Pages File Type
841168 Nonlinear Analysis: Theory, Methods & Applications 2011 7 Pages PDF
Abstract

In this paper, we consider the following nonlinear eigenvalue problems for the pp-Laplacian: −div(a(x)|∇u|p−2∇u)=λf(x,u)+μg(x,u)in Rnλ,μ>0,lim|x|→∞u=0, where 10λ,μ>0, aa is a measurable bounded function, and ff and gg are nonlinearities having subcritical growth with respect to uu. We prove multiple nontrivial solutions using a recent principle of Ricceri (2009) [10]. A regularity result is also established.

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