On solutions of semilinear elliptic equation with linear growth nonlinearity in $\mathbb{R}^N$

Abstract

We study nontrivial solutions for a class of semilinear ellipticequation which could be resonant at infinity. We establish theexistence of solutions for the equation by considering the modifiednon-resonant problem associated with the original equation throughMorse theory. Moreover, only linear growth assumption is imposed onthe nonlinearity and condition on the potential is weaker than thecoercive assumption.