Existence and Liouville-type theorems for some indefinite quasilinear elliptic problems with potentials vanishing at infinity

We study the existence versus absence of nontrivial weak solutions for a class of indefinite quasilinear elliptic problems on unbounded domains with noncompact boundary, in the presence of competing lower order nonlinearities with potentials decaying to zero at infinity. © 2009 Elsevier Inc. All rights reserved