Positive periodic solutions of the weighted p-laplacian with nonlinear sources

Abstract

In this paper we study the existence of time periodic solutions for the evolutionary weighted p-Laplacian with a nonlinear periodic source in a bounded domain containing the origin. We show that there is a critical exponent qc = qc(?, ?) =N(N++???)pp ? 1 and a singular exponent qs = p ? 1: there exists a positive periodic solution when 0 < q < qc and q = qs; while there is no positive periodic solution when q ? qc. The case when q = qs is completely different from the remaining case q = qs, the problem may or may not have solutions depending on the coefficients of the equation.