Electron. J. Diff. Equ., Vol. 2013 (2013), No. 11, pp. 1-16.

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

Adel Daouas, Ammar Moulahi

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.

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Adel Daouas
Mathematics department, College of sciences
Taibah University, Saudi Arabia
email: adaouas@taibahu.edu.sa
Ammar Moulahi
College of Business and Economics
Qassim University, Saudi Arabia
email: ammar.moulahi@fsm.rnu.tn

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