Equações elípticas com dependência não linear do gradiente

AUTOR(ES)
DATA DE PUBLICAÇÃO

2008

RESUMO

In this thesis we study the existence of solutions for elliptic equations with nonlinear dependence on the gradient of the solution. More precisely, we guarantee the existence of solution for the following classes of problems. (P1)_2u + q_u + _(x)u = f(x; u;ru;_u) in u(x) = 0; _u(x) = 0 on @; where _ RN;N _ 5, is a bounded smooth domain. (P2) uiv + qu00 + _(x)u = f(x; u; u0; u00) x 2 R: (P3)8<_u = h(x; u) + g(x;ru) in u >0 in u = 0 on @; where is a bounded, smooth domain in RN;N _ 3, the function h has sublinear and singular terms and g is bounded from above by a convection term of the type jruj_ with _ >0. (P4)Z uds + b jruj_ds _u = f(x; u;ru) em u(x) >0 em u(x) = 0 sobre @; where _; >0, a; b 2 R, _ RN, N _ 3, is a bounded, smooth domain and f : _ R _ RN ! R, H : R ! R are nonnegative continuous functions. In this work, the main techniques used to study these problems were: variational Techniques, Galerkin s method and Krasnoselskii s _xed point Theorem. Keywords: elliptic equations, nonlinear dependence on the gradient, variational techniques, Galerkin s Method, _xed point Theorem, bootstrap.

ASSUNTO(S)

galerkin, metodos de teses. equações diferenciais elipticas teses. matemática teses. teorema do ponto fixo (topologia).

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