Guglielmo Feltrin

Multiple positive solutions for a superlinear problem: a topological approach

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 λ1 as s→0+ and above λ1 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 topological degree which provides the multiplicity of solutions. Applications are given for u″+a(x)g(u)=0, where we prove the existence of 2n−1 positive solutions when a(x) has n positive humps and a−(x) is sufficiently large.

An application of coincidence degree theory to cyclic feedback type systems associated with nonlinear differential operators

Using Mawhins coincidence degree theory, we obtain some new continuation theorems which are designed to have as a natural application the study of the periodic problem for cyclic feedback type systems. We also discuss some examples of vector ordinary differential equations with a

Existence of positive solutions in the superlinear case via coincidence degree: the Neumann and the periodic boundary value problems

\phi

Pairs of positive periodic solutions of nonlinear ODEs with indefinite weight: a topological degree approach for the super-sublinear case

-Laplacian operator where our results can be applied.