Nonnegative solution of a class of double phase problems with logarithmic nonlinearity

Abstract

Abstract This manuscript proves the existence of a nonnegative, nontrivial solution to a class of double-phase problems involving potential functions and logarithmic nonlinearity in the setting of Sobolev space on complete manifolds. Some applications are also being investigated. The arguments are based on the Nehari manifold and some variational techniques.

Keywords

• Double-phase problem
• Existence of solutions
• Sobolev space on Riemannian manifold
• Variational method