Maria J. Alves, Ronaldo B. Assuncao, Paulo C. Carriao, Olimpio H. Miyagaki
Abstract:
In this article, we study the degenerate singular perturbation problems
for
small and
large positive,
where
with
.
We search for solutions that decay to zero as
,
when g is superlinear in the potential function changes signs.
We prove the existence of bound state solutions for degenerate,
singular, semilinear elliptic problems.
Additionally, when the nonlinearity g(x,u) is an odd function of u,
we obtain infinitely many geometrically distinct solutions.
Submitted September 22, 2011. Published June 27, 2012.
Math Subject Classifications: 35J20, 35J61, 35J70, 35J75, 35P10, 35P30.
Key Words: Semilinear degenerate elliptic equation; singular perturbation;
variational method; sign-changing potential;
nonlinear Schrodinger equation; bound state solution.
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Maria J. Alves Departamento de Matemática Universidade Federal de Minas Gerais, UFMG Av. Antônio Carlos, 6627, Caixa Postal 702 CEP 30161-970, Belo Horizonte, MG, Brasil email: mariajose@ufmg.br | |
Ronaldo B. Assunção Departamento de Matemática Universidade Federal de Minas Gerais, UFMG Av. Antônio Carlos, 6627, Caixa Postal 702 CEP 30161-970, Belo Horizonte, MG, Brasil email: ronaldo@mat.ufmg.br | |
Paulo C. Carrião Departamento de Matemática Universidade Federal de Minas Gerais, UFMG Av. Antônio Carlos, 6627, Caixa Postal 702 CEP 30161-970, Belo Horizonte, MG, Brasil email: carrion@mat.ufmg.br | |
Olímpio H. Miyagaki Departamento de Matemática Universidade Federal de Juiz de Fora, UFJF Cidade Universitária, Bairro Martelos CEP 36036-330, Juiz de Fora, MG, Brasil email: ohmiyagaki@gmail.com |
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