Mohsen Timoumi, Infinitely many homoclinic solutions for fourth-order differential equations with locally defined potentials, Vol. 2021 (2021), Article ID 12, pp. 1-10.

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DOI: 10.23952/cot.2021.12

Received April 12, 2021; Accepted October 20, 2021; Published November 1, 2021

 

Abstract. In this paper, we are concerned with the existence of homoclinic solutions for a class of nonautonomous fourth-order differential equations u^{(4)}(x)+\omega u''(x)+a(x)u(x)=f(x,u(x)),  x\in\mathbb{R}. Using a symmetric mountain pass theorem established by Kajikiya, infinitely many homoclinic solutions of the system  are obtained when the function a is only steel bounded from below unnecessary coercive at infinity, and the potential F(x,u)=\int^{u}_{0}f(x,v)dv is only locally defined near the origin with respect to u. Our result extends some previously known results in the literature.

 

How to Cite this Article:

Mohsen Timoumi, Infinitely many homoclinic solutions for fourth-order differential equations with locally defined potentials, Communications in Optimization Theory, Vol. 2021 (2021), Article ID 12, pp. 1-10.