Advances in Differential Equations

A bifurcation problem of some nonlinear degenerate elliptic equations

Nobuyoshi Fukagai, Masayuki Ito, and Kimiaki Narukawa

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Abstract

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

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

Dates
First available in Project Euclid: 22 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366638677

Mathematical Reviews number (MathSciNet)
MR1606343

Zentralblatt MATH identifier
1023.35506

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

Citation

Fukagai, Nobuyoshi; Ito, Masayuki; Narukawa, Kimiaki. A bifurcation problem of some nonlinear degenerate elliptic equations. Adv. Differential Equations 2 (1997), no. 6, 895--926. https://projecteuclid.org/euclid.ade/1366638677.


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