Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Abstract

We present two results on existence of innitely many positive solutions to the Neumann problem ( pu + (x)juj p 2 u = f (x;u) in , @u=@ = 0 on @ , where R N is a bounded open set with sucien tly smooth boundary @ , is the outer unit normal vector to @ , p > 1, > 0, 2 L 1 ( ) with ess infx2 (x) > 0 and f : R!R is a Carath eodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.