Bifurcation of stable equilibria under nonlinear flux boundary condition with null average weight

DOI10.1016/j.jmaa.2016.03.073zbMath1339.35031OpenAlexW2324439220MaRDI QIDQ275288

Arnaldo Simal do Nascimento, Gustavo Ferron Madeira

Publication date: 25 April 2016

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.2016.03.073

zbMATH Keywords

nonlinear boundary conditionpositive solutionpopulation geneticsindefinite weightbifurcation of equilibriaLyapunov-Schmidt type reductionMorse lemmanonconstant stable equilibria

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Bifurcations in context of PDEs (35B32)

Related Items

Bifurcation in a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition ⋮ Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition ⋮ Stability and bifurcation of a reaction-diffusion-advection model with nonlinear boundary condition ⋮ Uniqueness of a positive solution for the Laplace equation with indefinite superlinear boundary condition ⋮ Steady-state bifurcation of a nonlinear boundary problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global structure of supercritical bifurcation with turning points for the logistic elliptic equation with nonlinear boundary conditions
• Positive steady states of an indefinite equation with a nonlinear boundary condition: existence, multiplicity, stability and asymptotic profiles
• Bifurcation of stable equilibria and nonlinear flux boundary condition with indefinite weight
• Exponentially stable equilibria to an indefinite nonlinear Neumann problem in smooth domains
• Bifurcation approach to a logistic elliptic equation with a homogeneous incoming flux boundary condition
• Nonnegative solutions to an elliptic problem with nonlinear absorption and a nonlinear incoming flux on the boundary
• An indefinite nonlinear diffusion problem in population genetics. I: Existence and limiting profiles
• An indefinite nonlinear diffusion problem in population genetics. II: Stability and multiplicity
• Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions
• Equilibria and global dynamics of a problem with bifurcation from infinity
• Parabolic evolution equations and nonlinear boundary conditions
• A selection-migration model in population genetics
• Stability of local minima and stable nonconstant equilibria
• A semilinear parabolic system for migration and selection in population genetics
• Evolution of a semilinear parabolic system for migration and selection in population genetics
• Bifurcation for a logistic elliptic equation with nonlinear boundary conditions: a limiting case
• Evolution of a semilinear parabolic system for migration and selection without dominance
• Existence and regularity for a nonlinear boundary flow problem of population genetics
• Bifurcation from simple eigenvalues
• On a nonlinear elliptic eigenvalue problem with neumann boundary conditions, with an application to population genetics
• Remarks on a non linear equation arising in population genetics
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds
• Spatial Ecology via Reaction‐Diffusion Equations
• MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS
• Bifurcation and stability of equilibria with asymptotically linear boundary conditions at infinity
• Sobolev Spaces
• Properties of the principal eigenvalues of a general class of non-classical mixed boundary value problems.