A note on quasilinear elliptic eigenvalue problems

Abstract

We study an eigenvalue problem by a non-smooth critical point theory. Under general assumptions, we prove the existence of at least one solution as a minimum of a constrained energy functional. We apply some results on critical point theory with symmetry to provide a multiplicity result.

Keywords

• Quasilinear elliptic differential systems
• Equivariant category
• Non-smooth critical point theory
• Eigenvalue problem
• Lagrange multipliers.