Bifurcation for nonlinear elliptic boundary value problems I.

Kazuaki Taira

Collectanea Mathematica (1996)

  • Volume: 47, Issue: 3, page 207-229
  • ISSN: 0010-0757

Abstract

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This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the linearized problem.

How to cite

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Taira, Kazuaki. "Bifurcation for nonlinear elliptic boundary value problems I.." Collectanea Mathematica 47.3 (1996): 207-229. <http://eudml.org/doc/40350>.

@article{Taira1996,
abstract = {This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the linearized problem.},
author = {Taira, Kazuaki},
journal = {Collectanea Mathematica},
keywords = {Bifurcación paramétrica; Problema de contorno; Ecuaciones diferenciales elípticas; Ecuaciones en derivadas parciales no lineales; simple eigenvalue; local static bifurcation; degenerate boundary value problems; nonlinear second-order elliptic differential operators; first eigenvalue},
language = {eng},
number = {3},
pages = {207-229},
title = {Bifurcation for nonlinear elliptic boundary value problems I.},
url = {http://eudml.org/doc/40350},
volume = {47},
year = {1996},
}

TY - JOUR
AU - Taira, Kazuaki
TI - Bifurcation for nonlinear elliptic boundary value problems I.
JO - Collectanea Mathematica
PY - 1996
VL - 47
IS - 3
SP - 207
EP - 229
AB - This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the linearized problem.
LA - eng
KW - Bifurcación paramétrica; Problema de contorno; Ecuaciones diferenciales elípticas; Ecuaciones en derivadas parciales no lineales; simple eigenvalue; local static bifurcation; degenerate boundary value problems; nonlinear second-order elliptic differential operators; first eigenvalue
UR - http://eudml.org/doc/40350
ER -

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