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Received August 13, 2019; Accepted February 11, 2020; Published February 27, 2020
Abstract. In this paper, we consider the following damped vibration system
, where , is a symmetric matrix valued function and . We prove the existence of infinitely many fast homoclinic solutions for the system when as , is neither coercive nor uniformly positive definite and is superquadratic at infinity in the second variable but does not satisfy the well-known superquadratic growth conditions like the Ambrosetti-Rabinowitz or the Fei’s conditions.
How to Cite this Article:
Mohsen Timoumi, Infinitely many fast homoclinic orbits for a class of superquadratic damped vibration systems, Journal of Nonlinear Functional Analysis, Vol. 2020 (2020), Article ID 8, pp.1-16.