A note on homoclinic solutions for a class of semilinear fourth-order differential equations without coercivity
by Adel Daouas
International Journal of Dynamical Systems and Differential Equations (IJDSDE), Vol. 8, No. 3, 2018

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.

Online publication date: Wed, 27-Jun-2018

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