Existence and Nonexistence for Elliptic Equation with Cylindrical Potentials, Subcritical Exponent and Concave Term

Mohamed El Mokhtar Ould El Mo

Abstract

In this paper, we consider the existence and nonexistence of non-trivial solutions to elliptic equations with cylindrical potentials, concave term and subcritical exponent. First, we shall obtain a local minimizer by using the Ekeland’s variational principle. Secondly, we deduce a Pohozaev-type identity and obtain a nonexistence result.