On some third order nonlinear boundary value problems: Existence, location and multiplicity results

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:339

Article

Minhos, Feliz Manuel¹ 

[1] Univ Evora, Dept Matemat, Ctr Invest Matemat & Aplica UE, P-7000671 Evora, Portugal

关键词: Nagumo-type conditions;    lower and upper solution;    topological degree;    Ambrosetti-Prodi problems;   

DOI  :  10.1016/j.jmaa.2007.08.005

来源: Elsevier

【 摘 要 】

We prove an Ambrosetti-Prodi type result for the third order fully nonlinear equation u''' (t) + f (t, u(t), u'(t), u ''(t)) = sp(t) with f : [0, 1] x R-3 -> R and p : [0, 1] -> R+ continuous functions, s is an element of R, under several two-point separated boundary conditions. From a Nagumo-type growth condition, an a priori estimate on u '' is obtained. An existence and location result will be proved, by degree theory, for S E R such that there exist lower and upper solutions. The location part can be used to prove the existence of positive solutions if a non-negative lower solution is considered. The existence, nonexistence and multiplicity of solutions will be discussed as s varies. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free