Problemas elípticos quasilineares envolvendo não-linearidades interagindo com autovalores de alta energia
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2019-03-13
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Universidade Federal de Goiás
Resumo
In this thesis, using variational methods, we obtain nontrivial solutions for the quasilinear elliptic
equations whose the nonlinear term interacts with high eigenvalues for the linear problem. Here
we consider also the cases where the nonlinearity is subcritical or critical. Due to the presence of
the quasilinear term in order to treat the problems proposed in the present work which becomes
infeasible using directly the functional energy due the fact that it does not well defined in the
Sobolev space $H^1(\mathbb(R)^N)$. Hence we apply a change variable obtaining an
auxiliary energy functional associated with a semilinear elliptic problem. For this functional is
possible to show the existence of a Linking structure taking into account several behaviors on the
potential. Furthermore, critical points for that functional are weak solutions of the semilinear
problem.
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SILVA, J. S. Problemas elípticos quasilineares envolvendo não-linearidades interagindo com autovalores de alta energia. 2019. 131 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2019.