Infinitely many homoclinic solutions for second-order discrete Hamiltonian systems

Abstract

In this paper, we study the second-order self-adjoint discrete Hamiltonian system

where is an real symmetric positive definite matrix for all , is unnecessarily positive definite for all and is indefinite sign. By using fountain theorem, we establish some new criteria to guarantee that the above system has infinitely many homoclinic solutions under the assumption that is superquadratic as . Our results generalize and improve some existing results in the literature.

Keywords::

• homoclinic solutions
• discrete Hamiltonian systems
• fountain theorem
• superquadratic

AMS Subject Classification::

• 37J45
• 39A12
• 58E05
• 70H05

Acknowledgements

This work is supported by the Innovation Fund Project for Graduate Student of Hunan Province (CX2012B110) and the Fundamental Research Funds for the Central Universities of Central South University (2012zzts004).

Notes

^1. Email: [email protected]