Existence of solutions to a class of quasilinear elliptic equations

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This paper is concerned with the existence and nonexistence of nontrivial solutions for a class of quasilinear elliptic equations in RN involving the p-Laplacian. By utilizing a change of variables, the quasilinear equations are reduced to semilinear equations, whose associated functionals satisfy the geometric hypotheses of the mountain pass theorem. We establish the existence of nontrivial solutions via Mountain-Pass theorem. Furthermore, by using a Pohozaev type identity we prove the nonexistence of nontrivial solution under certain conditions.