TY - JOUR
AU - Ying Wang,
AU - Ziheng Zhang,
PY - 2017/12/19
Y2 - 2022/09/30
TI - Homoclinic Solutions for Some Nonperiodic Fourth Order Differential Equations with Sublinear Nonlinearities
JF - Journal of Advances in Applied & Computational Mathematics
JA - J. Adv. App. Comput. Math.
VL - 4
IS - 1
SE - Articles
DO - 10.15377/2409-5761.2017.04.3
UR - https://www.avantipublishers.com/index.php/jaacm/article/view/837
SP - 15-22
AB - <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>
ER -