New homoclinic solutions for a class of second-order Hamiltonian systems with a mixed condition

Abstract

Abstract In this paper, we introduce a new mixed condition to obtain a new compact embedding theorem. Under this theorem, we study the existence and multiplicity of nontrivial homoclinic solutions for a class of second-order Hamiltonian systems with variable separated type nonlinear terms.

Keywords

• Homoclinic solutions
• Second-order Hamiltonian systems
• Mixed condition
• Embedding theorem
• Variational methods