Soluções positivas para uma classe de problemas elipticos quasilineares envolvendo expoentes criticos

AUTOR(ES)

Emerson Alves Mendonça de Abreu

DATA DE PUBLICAÇÃO

2001

RESUMO

Our work is divided in two parts. In the part I, we will study existence, multiplicity and nonexistence of positive solutions for a class of elliptic operators involving critical nonlinearities. We will work with this problems in the radial form, that us permit have a better vision of the phenomenon that occur. In that class of the operators are included the operators Laplacian, p-Laplacian and k-Hessian among others, and the nonlinearity are divided in critical and critical concaveconvexo In the second case, we showed the existence of the at least two solutions and we obtained too some new results of the nonexistence of the positive solutions. In part lI, we gave one variational solution for one conjecture of the Brézis-Nirenberg. We obtained some extensions of this conjecture. Another question aboard, was the calculus of the optimal constant for one Sobolev inequality with remainder terms

ASSUNTO(S)

problemas de equações diferenciais parciais dirichlet equações diferenciais elipticas

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