Olimpio Hiroshi Miyagaki, Sandra Imaculada Moreira, Ricardo Ruviaro
Abstract:
We establish existence and non-existence results for a quasilinear
asymptotically linear Schrodinger problem. In the first result,
we prove that a minimization problem constrained to the Pohozaev manifold
is not achieved. In the second, the main argument consists in a splitting
lemma for a functional constrained to the Pohozaev manifold.
Because of the lack of the monotonicity we are not able to project to
the usual Nehari manifold any longer, and this approach is crucial in
order to compare the critical level to reach a contradiction.
This argument was used in [21, 24, 32] for semilinear equations and
in [11] for quasilinear equations.
Submitted August 27, 2017. Published September 11, 2018.
Math Subject Classifications: 35J10, 35J20, 35J60, 35Q55.
Key Words: Quasilinear Schrodinger equations; variational methods;
asymptotically linear
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Olimpio Hiroshi Miyagaki Universidade Federal de Juiz de Fora Departamento de Matemática 36036-330 Juiz de Fora-MG, Brazil email: ohmiyagaki@gmail.com |
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Sandra Imaculada Moreira Universidade Estadual do Maranhão Departamento de Matemática e Informática 65055-900 São Luís-MA, Brazil email: ymaculada@gmail.com |
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Ricardo Ruviaro Universidade de Brasília Departamento de Matemática 70910-900 Brasília-DF, Brazil email: ricardoruviaro@gmail.com |
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