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Título del libro: Analysis And Topology In Nonlinear Differential Equations: A Tribute To Bernhard Ruf On The Occasion Of His 60th Birthday
Título del capítulo: A Supercritical Elliptic Problem in a Cylindrical Shell

Autores UNAM:
MONICA ALICIA CLAPP JIMENEZ LABORA;
Autores externos:

Idioma:

Año de publicación:
2014
Palabras clave:

Nonlinear elliptic equation; supercritical nonlinearity; unbounded domain


Resumen:

We consider the problem -Delta u = vertical bar u vertical bar(p-2) u in Omega, u=0 on partial derivative Omega, where Omega := {(y,z) is an element of Rm+1 x RN-m-1 : 0 < a < vertical bar y vertical bar < b < infinity, 0 <= m <= N - 1 and N >= 2. Let 2(N,m)* := 2(N - m)/(N - m - 2) if m < N - 2 and 2(N,m)* := infinity if m = N - 2 or N - 1. We show that 2(N,m)* is the true critical exponent for this problem, and that there exist nontrivial solutions if 2 < p < 2(N,m)* but there are no such solutions if p >= 2(N,m)*.


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