Nontrivial solutions for a class of Hamiltonian strongly degenerate elliptic system

Abstract

In this paper, we study the existence of nontrivial to the following Hamiltonian strongly degenerate elliptic system in whole space where are nonnegative functions with and V might unbounded or vanish at infinity. Here is the strongly degenerate operator and the nonlinearity terms are continuous functions and satisfy some assumptions that will be specified later. Due to the unbounded or vanishing of potentials and degeneracy of the operator, some new compact embedding theorems are used in the proof. Our results extend and generalize some existing results.