@article{Ying Wang_Ziheng Zhang_2017, title={Homoclinic Solutions for Some Nonperiodic Fourth Order Differential Equations with Sublinear Nonlinearities}, volume={4}, url={https://www.avantipublishers.com/index.php/jaacm/article/view/837}, DOI={10.15377/2409-5761.2017.04.3}, abstractNote={<p>In this paper we investigate the existence of homoclinic solutions for the following fourth order nonautonomous differential equations; <em>u</em><sup>(4)</sup> <em>+ wu’’ + a(x)u = f (x,u), (FDE)</em> where <em>w</em> is a constant, <em>a</em> <em>ɛ C</em>(<em>R, R</em>) and <em>f</em> <em>ɛ</em> <em>C</em>(<em>R x R, R</em>) . The novelty of this paper is that, when (FDE) is nonperiodic, i.e., <em>a</em> and <em>f</em> are nonperiodic in <em>x</em>, assuming that <em>a</em> is bounded from below and <em>f</em> is sublinear as | <em>u</em> |→ +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.</p>}, number={1}, journal={Journal of Advances in Applied & Computational Mathematics}, author={Ying Wang and Ziheng Zhang}, year={2017}, month={Dec.}, pages={15–22} }