On Hamiltonian elliptic systems with exponential growth in dimension two
In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hami...
| Autor: | |
|---|---|
| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2017 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-02082017-150001 |
| Acceso en línea: | http://www.teses.usp.br/teses/disponiveis/55/55135/tde-02082017-150001/ |
| Access Level: | acceso abierto |
| Palabra clave: | Crescimento exponencial Desigualdade de Trudinger - Moser Espaços de Lorent-Sobolev Exponential growth Hamiltonian systems Lorentz-Sobolev spaces Métodos variacionais Sistemas hamiltonianos Trudinger-Moser inequality Variational methods |
| Sumario: | In this work we study the existence of nontrivial weak solutions for some Hamiltonian elliptic systems in dimension two, involving a potential function and nonlinearities which possess maximal growth with respect to a critical curve (hyperbola). We consider four different cases. First, we study Hamiltonian systems in bounded domains with potential function identically zero. The second case deals with systems of equations on the whole space, the potential function is bounded from below for some positive constant and satisfies some integrability conditions, while the nonlinearities involve weight functions containing a singulatity at the origin. In the third case, we consider systems with coercivity potential functions and nonlinearities with weight functions which may have singularity at the origin or decay at infinity. In the last case, we study Hamiltonian systems, where the potential can be unbounded or can vanish at infinity. To establish the existence of solutions, we use variational methods combined with Trudinger-Moser type inequalities for Lorentz-Sobolev spaces and a finite-dimensional approximation. |
|---|