Multiplicity results for some quasilinear elliptic problems with concave nonlinearities

Abstract The purpose of this paper is to investigate the existence of five nontrivial solutions and the existence of infinitely many nontrivial solutions for a class of (p, 2)-Laplacian equations with subcritical polynomial growth and subcritical (critical) exponential growth. Some existence results for nontrivial solutions are established by using the variational methods.