(p,2)-equations asymmetric at both zero and infinity

Abstract

AbstractWe consider a {(p,2)}-equation, that is, a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian with {p>2}. The reaction term is {(p-1)}-linear, but exhibits asymmetric behavior at {\pm\infty} and at {0^{\pm}}. Using variational tools, together with truncation and comparison techniques and Morse theory, we prove two multiplicity theorems, one of them providing sign information for all the solutions (positive, negative, nodal).