Multiple positive solutions for a superlinear problem: A topological approach

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:259

Article

Feltrin, Guglielmo¹  Zanolin, Fabio² 

[1] SISSA Int Sch Adv Studies, I-34136 Trieste, Italy

[2] Univ Udine, Dept Math & Comp Sci, I-33100 Udine, Italy

关键词: Positive solutions;    Superlinear equations;    Indefinite weight;    Multiplicity results;    Boundary value problems;   

DOI  :  10.1016/j.jde.2015.02.032

来源: Elsevier

【 摘 要 】

We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u '' + f (x, u) = 0. We allow x 1 -> f (x, s) to change its sign in order to cover the case of scalar equations with indefinite weight. Roughly speaking, our main assumptions require that f (x, s)/s is below lambda(1) as s -> 0(+) and above lambda(1) as s -> +infinity. In particular, we can deal with the situation in which f (x, s) has a superlinear growth at zero and at infinity. We propose a new approach based on topological degree which provides the multiplicity of solutions. Applications are given for u '' + a(x)g(u) = 0, where we prove the existence of 2(n) + 1 positive solutions when a(x) has n positive humps and a (x) is sufficiently large. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free