**Title: **Multiple positive solutions for a superlinear problem: a topological approach

**Abstract: **
I will present a recent joint work with Fabio Zanolin.

We study the existence and 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 the first eigenvalue for s near zero and above the first eigenvalue for s near 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 its negative part is sufficiently large.

This seminar is part of the AJS series of seminars.