01194nas a2200121   4500008004100000245008200041210006900123260001300192520077400205100002300979700001901002856005101021       2015                        en  d00aMultiple positive solutions for a superlinear problem: a topological approach0 aMultiple positive solutions for a superlinear problem a topologi  bElsevier3 a<p>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 ↦ 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→0^+ and above λ_1 as s→+∞. 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'' + 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.</p>1 aFeltrin, Guglielmo1 aZanolin, Fabio  uhttp://urania.sissa.it/xmlui/handle/1963/35147