Multiple nonnegative solutions for an elliptic boundary value problem involving combined nonlinearities
Let p > 1, q > p, s is an element of]1, p[, r is an element of ]1, s[ and let lambda, mu be real positive parameters. We establish a multiplicity result for the problem -Delta(p)u = lambda u(s-1) - mu u(r-1) + u(q-1) in Omega, u(vertical bar partial derivative Omega) = 0 by means of variational methods. In particular, for lambda and mu small enough, the existence of at least two nonzero and nonnegative solutions is obtained. If q is less than the critical exponent, we also get the existence of a third nonzero and nonnegative solution. (C) 2010 Elsevier Ltd. All rights reserved.
nonnegative solutions elliptic boundary value problems combined nonlinearities variational methods