A study of nonlinear problems for the p-Laplacian in Rn via Ricceri's principle

In this paper, we consider the following nonlinear eigenvalue problems for the p-Laplacian: -div (a(x)vertical bar del u vertical bar(p-2)del u) = lambda f(x, u) + mu g(x, u) in R-n lambda, mu > 0, lim(vertical bar x vertical bar ->infinity) u = 0, where 1 < p < n, lambda, mu > 0, a is a measurable bounded function, and f and g are nonlinearities having subcritical growth with respect to u. We prove multiple nontrivial solutions using a recent principle of Ricceri (2009) [10]. A regularity result is also established. (c) 2011 Elsevier Ltd. All rights reserved.