#### Mohsen Timoumi, Infinitely many homoclinic solutions for a class of superquadratic fourth-order differential equations, Vol. 2018 (2018), Article ID 20, pp. 1-12

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DOI: 10.23952/jnfa.2018.20

Received October 25, 2017; Accepted May 7, 2018; Published May 22, 2018

Abstract. Using a variant fountain theorem, we prove the existence of infinitely many homoclinic solutions of a class of fourth-order differential equations $u^4(x)+\omega u''(x)+a(x)u(x)=f(x,u(x)),$ $\forall x\in\mathbb{R},$ where $a\in C(\mathbb{R}, \mathbb{R})$ may be negative on a bounded interval and $F(x,u)=\int^{u}_{0}f(x,t)dt$ is superquadratic at infinity in the second variable but does not need to satisfy the known Ambrosetti-Rabinowitz superquadratic growth condition.