Existence of infinitely many homoclinic orbits for second-order systems involving Hamiltonian-type equations

Abstract

We study the second-order differential system $$ ddot u + Adot{u}- L(t)u+ abla V(t,u)=0, $$ where A is an antisymmetric constant matrix and $L in C(mathbb{R}, mathbb{R}^{N^2})$. We establish the existence of infinitely many homoclinic solutions if W is of subquadratic growth as $|x| o +infty$ and L does not satisfy the global positive definiteness assumption. In the particular case where A=0, earlier results in the literature are generalized.

Keywords

• Homoclinic solutions
• differential system
• critical point