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.

%B J. Differential Equations 259 (2015), 925–963. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/35147 %1 35387 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-17T09:31:06Z No. of bitstreams: 1 FeltrinZanolin_jde2015.pdf: 350880 bytes, checksum: 0e329b01081df570863ea2492ffefe0a (MD5) %R 10.1016/j.jde.2015.02.032