Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: a limiting case.

Producción CyT

Artículo

Autoría

RAMOS QUOIRIN, HUMBERTO RODRIGO ; Kenichiro Umezu

Fecha

2015

Editorial y Lugar de Edición

ACADEMIC PRESS INC ELSEVIER SCIENCE

Revista

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ACADEMIC PRESS INC ELSEVIER SCIENCE

Resumen Información suministrada por el agente en SIGEVA

We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. ... We investigate bifurcation from the zero solution for a logistic elliptic equation with a sign-definite nonlinear boundary condition. In view of the lack of regularity of the term on the boundary, the abstract theory on bifurcation from simple eigenvalues due to Crandall and Rabinowitz does not apply. A regularization procedure and a topological method due to Whyburn are used to prove the existence and the global behavior at infinity of a subcontinuum of nontrivial non-negative weak solutions. The direction of the bifurcation component at zero is also investigated. This paper treats a limiting case of our previous work [19], where the case of sign-changing nonlinear boundary conditions is considered.

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Palabras Clave

Semilinear elliptic problem;Bifurcation;Positive solution;Nonlinear boundary condition