Global structure of supercritical bifurcation with turning points for the logistic elliptic equation with nonlinear boundary conditions

DOI10.1016/J.NA.2013.05.011zbMath1283.35027OpenAlexW1990793175MaRDI QIDQ395403

Kenichiro Umezu

Publication date: 29 January 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2013.05.011

zbMATH Keywords

nonlinear boundary conditionpositive solutionglobal bifurcationnonlinear elliptic equationblow up argumentlogistic nonlinearitysubcontinuum

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Population dynamics (general) (92D25) Bifurcations in context of PDEs (35B32) Semilinear elliptic equations (35J61)

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Cites Work

• 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
• Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions
• Mixed boundary value problems for elliptic and parabolic differential equations of second order
• On the existence of positive eigenfunctions for an eigenvalue problem with indefinite weight function
• Blow up results and localization of blow up points for the heat equation with a nonlinear boundary condition
• Bifurcation from simple eigenvalues
• Local and global bifurcation results for a semilinear boundary value problem
• Localization on the Boundary of Blow-up for Reaction–Diffusion Equations with Nonlinear Boundary Conditions
• EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO ELLIPTIC PROBLEMS WITH SUBLINEAR MIXED BOUNDARY CONDITIONS
• Diffusive logistic equations with indefinite weights: population models in disrupted environments
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• On principal eigenvalues for boundary value problems with indefinite weight and Robin boundary conditions
• Spatial Ecology via Reaction‐Diffusion Equations
• MULTIPLICITY OF POSITIVE SOLUTIONS UNDER NONLINEAR BOUNDARY CONDITIONS FOR DIFFUSIVE LOGISTIC EQUATIONS
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