A quasilinear parabolic perturbation of the linear heat equation

DOI10.1016/j.jde.2011.09.018zbMath1230.35052OpenAlexW2009733631MaRDI QIDQ649758

Santiago Cano-Casanova, Kazuhiro Takimoto, Julián López-Gómez

Publication date: 6 December 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.09.018

zbMATH Keywords

dynamicsmean curvature flow operatorpositive steady-statesquasilinear heat equation

Mathematics Subject Classification ID

Heat equation (35K05) Quasilinear parabolic equations (35K59) Quasilinear parabolic equations with mean curvature operator (35K93)

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Cites Work

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• Algebraic multiplicity of eigenvalues of linear operators
• Optimal multiplicity in local bifurcation theory. I: Generalized generic eigenvalues
• The maximum principle for cooperative weakly coupled elliptic systems and some applications
• Bounded components of positive solutions of abstract fixed point equations: Mushrooms, loops and isolas
• The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Some global results for nonlinear eigenvalue problems
• Bifurcation from simple eigenvalues
• Topics in stability and bifurcation theory
• BIFURCATION FROM SIMPLE EIGENVALUES AND EIGENVALUES OF GEOMETRIC MULTIPLICITY ONE
• A bifurcation problem for a quasi-linear elliptic boundary value problem