On the existence and non-existence of bounded solutions for a fourth order ODE

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Mosconi, Sunra J. N.¹  Santra, Sanjiban² 

[1] Univ Catania, Dipartimento Matemat & Informat, I-95125 Catania, Italy

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

关键词: Fourth order equations;    Bounded solutions;    Periodic solutions;    Extended FisherKolmogorov equation;   

DOI  :  10.1016/j.jde.2013.08.001

来源: Elsevier

【 摘 要 】

We prove that if F is an element of C-1 (R) is coercive and {F' =0} is discrete, then the EFK equation u''' - c(2)u '' + F'(u) = 0 (1) possesses L-infinity(R) solutions if and only if F' changes sign at least twice. As a corollary we prove that if u(n) solves u(n)'''' + c(n)(2)u(n)'' + F'(u(n)) = 0, then parallel to u(n)parallel to(infinity) -> +infinity if c(n) -> 0, provided F has a unique local minimum, its only minimum is nondegenerate and int({F' = 0}) = 0. Finally we give criteria ensuring existence and non-existence of T-periodic solutions to (1) when F has multiple wells. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free