Special Session 14: New perspectives in the qualitative study of nonlinear differential equations and dynamical systems

Global multiplicity results in a Moore-Nehari type problem
Eduardo Mu\~noz-Hern\`andez
Complutense University of Madrid
Spain
Co-Author(s):    Juli\`an L\`opez-G\`omez and Fabio Zanolin
Abstract:
In this talk, we present a superlinear problem of the Moore-Nehari type. If there is a general non-negative weight in front of the nonlinear term, existence of positive and nodal solutions is guaranteed by classical bifurcation methods. On the other hand, if we restrict ourselves to the analysis of positive solutions for a symmetric non-negative weight vanishing in the middle interval, i.e., to the classical setting of the Moore-Nehari problem, it is possible to prove multiplicity of positive solutions for both signs of the bifurcation parameter. This is a joint work with Professors Juli\`an L\`opez-G\`omez (Complutense University of Madrid) and Fabio Zanolin (University of Udine).