Spectral Theory Approach for a Class of Indefinite Variational Problems
Expositor: Mayra Soares
Data e Horário: 09/06/19 | 16:00h
RESUMO: An abstract linking theorem for Cerami sequences is developed with the purpose of handling indefinite problems by variational approach, especially nonlinear Schrdinger equations with sign-changing potentials and asymptotically linear nonlinearities. In order to find a nontrivial solution to the problem under discussion, we apply the abstract result to the associated indefinite functional and obtain a nontrivial critical point to such a functional. This critical point is going to be a weak solution to the problem, as desired. Spectral theory is the main tool used in this work. Exploiting spectral properties of the elliptic operator associated to the problem in question, it enables to establish a linking structure on the Hilbert space where the mentioned critical points are sought.