In this article, we prove the existence and multiplicity of nontrivial solutions for the nonperiodic perturbed fractional Hamiltonian systems
where is a parameter, , and are left and right Liouville-Weyl fractional derivatives of order on the whole axis respectively, the matrix is not necessary positive definite for all nor coercive, and small enough. Replacing the Ambrosetti-Rabinowitz Condition by general superquadratic assumpt ions, we establish the existence and multiplicity results for the above system. Some examples are also given to illustrate our results.
Submitted December 13, 2016. Published March 30, 2017.
Math Subject Classifications: 34C37, 35A15, 37J45.
Key Words: Fractional Hamiltonian systems; critical point; variational methods.
Show me the PDF file (271 KB), TEX file for this article.
| Abderrazek Benhassine |
Dept. of Mathematics
High Institut of Informatics and Mathematics
5000, Monastir, Tunisia
Return to the EJDE web page