Homoclinic Solutions for Some Nonperiodic Fourth Order Differential Equations with Sublinear Nonlinearities - Ying Wang; Ziheng Zhang (Journal of Advances in Applied & Computational Mathematics, 2017)
In this paper we investigate the existence of homoclinic solutions for the following fourth order nonautonomous differential equations; u(4) + wu’’ + a(x)u = f (x,u), (FDE) where w is a constant, a ɛ C(R, R) and f ɛ C(R x R, R) . The novelty of this paper is that, when (FDE) is nonperiodic, i.e., a and f are nonperiodic in x, assuming that a is bounded from below and f is sublinear as | u |→ +ꚙ , we establish one new criterion to guarantee the existence and multiplicity of homoclinic solutions of (FDE). Recent results in the literature are generalized and improved.