Existence of infinitely many solutions for pp-Laplacian equations in RNRN

•We give a direct sum decomposition of the Sobolev space corresponding to the quasilinear elliptic problem.•We obtain the existence of infinitely many solutions of the quasilinear elliptic problem.•We establish new theorems under weaker assumptions on the nonlinearity.

Based on the cohomological linking method for cones and a new direct sum decomposition of W1,p(RN)W1,p(RN), we study the existence and multiplicity of solutions of a pp-Laplacian equation in RNRN with sign-changing potential and subcritical pp-superlinear nonlinearity. Our assumptions are mild and different from those studied previously.