@article {2015,
title = {Multiple positive solutions for a superlinear problem: a topological approach},
journal = {J. Differential Equations 259 (2015), 925{\textendash}963.},
number = {Journal of Differential Equations;volume 259; issue 3; pages 925-963;},
year = {2015},
note = {Work presented at the "Special Session 21" of the "10th AIMS Conference on Dynamical Systems, Differential Equations and Applications" (Madrid, July 7-11, 2014).},
publisher = {Elsevier},
abstract = {We study the multiplicity of positive solutions for a two-point boundary value problem associated to the nonlinear second order equation u{\textquoteright}{\textquoteright}+f(x,u)=0. We allow x ↦ 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 λ_1 as s{\textrightarrow}0^+ and above λ_1 as s{\textrightarrow}+$\infty$. 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 the topological degree which provides the multiplicity of solutions. Applications are given for u{\textquoteright}{\textquoteright} + 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.},
doi = {10.1016/j.jde.2015.02.032},
url = {http://urania.sissa.it/xmlui/handle/1963/35147},
author = {Guglielmo Feltrin and Fabio Zanolin}
}