Multiple positive solutions for semi-linear elliptic systems involving sign-changing weight

摘要

In this paper, we study the multiplicity results of positive solutions for a semi-linear elliptic system involving critical growth terms. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we investigate how the coefficient h(x) of the critical nonlinearity affects the number of positive solutions of that problem and get a relationship between the number of positive solutions and the topology of the global maximum set of h. Copyright (c) 2014 John Wiley & Sons, Ltd.