Global existence of branches of stationary solutions for a system of reaction diffusion equations from biology

DOI10.1016/0362-546X(81)90097-3zbMath0471.35031MaRDI QIDQ3924578

Franz Rothe

Publication date: 1981

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

maximum principlepattern formationreaction-diffusion equationsglobal bifurcation theoryexistence of stationary solutionsDirichlet- or Neumann-boundary conditionvariational method of Ljusternik-Schnirelman

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Variational methods applied to PDEs (35A15) Maximum principles in context of PDEs (35B50) Variational methods for elliptic systems (35J50) Bifurcations in context of PDEs (35B32)

Related Items (16)

An iterative method for the solution of some semilinear elliptic systems with discontinuities ⋮ Existence and multiplicity of solutions for semilinear elliptic systems ⋮ A numerical verification method for two-coupled elliptic partial differential equations ⋮ Bifurcation from infinity and multiplicity results for an elliptic system from biology ⋮ A variational approach to noncooperative elliptic systems ⋮ Existence results for some nonlinear elliptic systems ⋮ Non-resonance and existence for systems of non-linear operator equations ⋮ Positive solutions of some coercive-anticoercive elliptic systems ⋮ Nonzero solutions of a nonlinear elliptic system at resonance ⋮ Lyapunov functionals and stability for FitzHugh-Nagumo systems ⋮ Multiple solutions for asymptotically linear elliptic systems ⋮ Solutions of systems of elliptic differential equations on circular domains ⋮ Stability Criteria for Reaction-Diffusion Systems with Skew-Gradient Structure ⋮ Existence results for the positive solutions of nonlinear elliptic systems ⋮ Existence of the minimal positive solution of some nonlinear elliptic systems when the nonlinearity is the sum of a sublinear and a superlinear term ⋮ On steady state solutions of a system of reaction-diffusion equations from biology

Cites Work

• Unnamed Item
• A simple system of reaction-diffusion equations describing morphogenesis: Asymptotic behavior
• Reaction-diffusion equation describing morphogenesis. I: Waveform stability of stationary wave solutions in a one dimensional model
• Bifurcation analysis of nonlinear reaction diffusion equations I. Evolution equations and the steady state solutions
• Stability results for a class of non-linear parabolic equations
• Some global results for nonlinear eigenvalue problems
• Some aspects of nonlinear eigenvalue problems
• A Singular Perturbation Analysis for a Reaction-Diffusion System Describing Pattern Formation
• A comparison technique for systems of reaction-diffusion equations
• The chemical basis of morphogenesis

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