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.