8 Giugno, 2016 16:15 in punto

Sezione di Analisi

Multiple Neumann solutions of some second order ODEs with indefinite weight

Maurizio Garrione, Università degli Studi di Milano-Bicocca

Aula seminari 3° piano

We consider the Neumann problem associated with the scalar second order ODE u''+q(t)g(u)=0, where q is a sign-changing weight and g is a positive function satisfying sublinear growth assumptions. Through the use of a suitable change of variables, the problem is led back to the study of Neumann solutions for a forced perturbation of an autonomous planar system, which we study by means of a shooting technique. We illustrate results of existence and multiplicity of solutions depending in a quite precise way on mean properties of the weight.