The method of upper and lower solutions for diffraction problems of quasilinear elliptic reaction-diffusion systems

DOI10.1016/j.jmaa.2011.02.050zbMath1216.35061OpenAlexW1978307820MaRDI QIDQ534758

Qi-Jian Tan, Zhong-Jian Leng

Publication date: 10 May 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.02.050

zbMATH Keywords

upper and lower solutionsreaction-diffusionquasilinear elliptic systemsdiffraction problem

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25) PDEs with low regular coefficients and/or low regular data (35R05) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62)

Related Items (5)

A quasilinear transmission problem with application to Maxwell equations with a divergence-free \(\mathcal{D} \)-field ⋮ Nonlinear Operators, Fixed-Point Theorems, Nonlinear Equations ⋮ Diffraction problems for quasilinear parabolic systems with boundary intersecting interfaces ⋮ An elliptic cross-diffusion system describing two-species models on a bounded domain with different natural conditions ⋮ An elliptic problem with strongly nonlinear interface condition

Cites Work

• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• Positive solutions of quasilinear parabolic systems with nonlinear boundary conditions
• The regularity of generalized solutions for the \(n\)-dimensional quasi-linear parabolic diffraction problems
• Quasilinear reaction-diffusion systems with nonlinear boundary conditions
• Diffraction problems for quasilinear reaction--diffusion systems.
• Linear and quasilinear elliptic equations
• A necessary and sufficient condition for global existence for a quasilinear reaction-diffusion system
• Nonlinear elliptic boundary-value problems in unbounded domains
• A maximum principle for semilinear parabolic systems and applications
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