Title: A note on homoclinic solutions for a class of semilinear fourth-order differential equations without coercivity

Authors: Adel Daouas

Addresses: Department of Mathematics, High School of Sciences and Technology, Hammam Sousse 4011, Tunisia

Abstract: In this paper, we study the existence of homoclinic solutions for a class of fourth-order nonautonomous differential equations. Indeed, without coercive condition on the coefficient of the linear term and under suitable assumptions on the growth of the linearity, we establish the existence and the multiplicity of homoclinic solutions by using the Mountain Pass Theorem. Some recent results in the literature are generalized. Particularly, the open problem proposed by Zhang and Yuan (2015) is solved.

Keywords: fourth-order differential equations; homoclinic solutions; Mountain Pass Theorem.

DOI: 10.1504/IJDSDE.2018.092673

International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.3, pp.204 - 216

Accepted: 02 Aug 2017
Published online: 27 Jun 2018 *

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