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.
International Journal of Dynamical Systems and Differential Equations, 2018 Vol.8 No.3, pp.204 - 216
Received: 17 Dec 2016
Accepted: 02 Aug 2017
Published online: 06 Dec 2017 *