Advances in Differential Equations

A bifurcation problem of some nonlinear degenerate elliptic equations

Nobuyoshi Fukagai, Masayuki Ito, and Kimiaki Narukawa

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A bifurcation problem or a nonlinear eigenvalue problem for degenerate quasilinear elliptic equations with Dirichlet boundary condition is studied. Uniform estimates of partial derivatives of solutions are calculated. By virtue of these estimatates, we can apply the Leray-Schauder degree theory to our problem and obtain the bifurcation of nontrivial weak solutions.

Article information

Adv. Differential Equations, Volume 2, Number 6 (1997), 895-926.

First available in Project Euclid: 22 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 34B15: Nonlinear boundary value problems 35B32: Bifurcation [See also 37Gxx, 37K50] 47H15


Fukagai, Nobuyoshi; Ito, Masayuki; Narukawa, Kimiaki. A bifurcation problem of some nonlinear degenerate elliptic equations. Adv. Differential Equations 2 (1997), no. 6, 895--926.

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