Nonhomogeneous semilinear elliptic systems

Author(s)

Ederson Moreira Dos Santos

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2007-10-10

Examining board members

Djairo Guedes de Figueiredo; Marcelo da Silva Montenegro; Jose Valdo Abreu Gonçalves; Arnaldo Simal do Nascimento; Marcelo Fernandes Furtado

• Advisor: Francisco Odair Vieira de Paiva; Djairo Guedes de Figueiredo

Abstract

In this work we consider two classes of nonhomogeneous systems, where in certain cases one of these classes turns to be a gradient system, while the other one becomes a system of Hamiltonian type. We are concerned about the questions of existence, nonexistence, uniqueness and multiplicity of solutions. To obtain our results we apply the method of subsolutions and supersolutions, minimization of functionals, the Lagrange multiplier theorem, the Mountain Pass Theorem, a Riesz¿s representation theorem for certain Sobolev spaces and the Concentration-Compactness Principle (AU)