Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 11, pp. 1-16.
Title: Existence of infinitely many homoclinic orbits for second-order
systems involving Hamiltonian-type equations
Authors: Adel Daouas (Taibah Univ., Saudi Arabia)
Ammar Moulahi (Qassim Univ., Saudi Arabia)
Abstract:
We study the second-order differential system
$$
\ddot u + A\dot{u}- L(t)u+ \nabla V(t,u)=0,
$$
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 $|x| \to +\infty$ and L does not satisfy the global
positive definiteness assumption. In the particular case where A=0,
earlier results in the literature are generalized.
Submitted March 25, 2012. Published January 14, 2013.
Math Subject Classifications: 34C37, 37J45, 70H05.
Key Words: Homoclinic solutions; differential system; critical point.