A note on homoclinic solutions for a class of semilinear fourth-order differential equations without coercivity (Q2289550)

Summary: 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 \textit{Z. Zhang} and \textit{R. Yuan} [Appl. Math. Comput. 250, 280--286 (2015; Zbl 1328.34040)] is solved.