On the Fredholm alternative for the p-Laplacian

摘要

In this paper we study the range of the operator u→(p−1)−1(|u′|p−2u′)′+α|u+|p−2u+−β|u−|p−2u−, u(0)=u(T)=0, p>1, πp=(2π/psin(π/p)), α>0, β>0 and (p−1)1/p(α−(1/p)+β−(1/p))=2. The results of this paper generalize the corresponding results obtained in [J. Differential Equations 151 (1999) 386] and the method used in this paper is elementary.