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High multiplicity of positive solutions to indefinite boundary value problems: a topological approach

Speaker: 
Guglielmo Feltrin
Institution: 
SISSA
Schedule: 
Thursday, May 12, 2016 - 16:15 to 18:00
Location: 
A-136
Abstract: 

In some recent works in collaboration with F. Zanolin (Udine) and A. Boscaggin (Torino) we deal with positive solutions to boundary value problems associated with second order non-linear differential equations of the form u'' + a(t)g(u) = 0, where g(u) is a positive nonlinearity and a(t) is a sign-changing weight. In the seminar, we focus mainly on the periodic problem and on a non-linearity g(u) with superlinear growth at zero and at infinity. We prove the existence of 2^m-1 positive periodic solutions when a(t) has m positive humps separated by m negative ones (in a periodicity interval) and the negative part of a(t) is sufficiently large. Furthermore, we consider subharmonic solutions and solutions with complex behaviour. The proof is based on the topological degree and applies also to the super-sublinear case and to Dirichlet/Neumann problems.

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