Bifurcation for nonlinear elliptic boundary value problems I

• Autores: Kazuaki Taira
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 47, Fasc. 3, 1996, págs. 207-229
• Idioma: inglés
• Enlaces
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• Resumen

  • This paper is devoted to local static bifurcation theory for a class of \textit{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 \textit{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.

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