The local stability of positive solutions to the Hammerstein equation with a nonmonotonic Nemytskii operator

DOI10.1007/BF01295289zbMath0671.47045OpenAlexW2913638767MaRDI QIDQ1119891

Peter Takáč

Publication date: 1988

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/178407

zbMATH Keywords

Hammerstein equationlocal stability of a nonzero positive solutionlocal stability on secondary bifurcationsoperators on Banach latticesspectral radius of the Fréchet derivativespectral theory for completely continuous and irreducible positivespectral theory for completely continuous and irreducible positive operators on Banach lattices

Mathematics Subject Classification ID

Stability theory for integral equations (45M10) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07)

Related Items (2)

Convergence in the part metric for discrete dynamical systems in ordered topological cones ⋮ Dispersion population models discrete in time and continuous in space

Cites Work

• Multiple fixed point theorems for problems in chemical reactor theory
• On a class of Hammerstein integral equations
• Irreducible compact operators
• A global bifurcation theorem with applications to functional differential equations
• Supersolutions, monotone iterations, and stability
• Transversality and cone maps
• Global solution branches for positive mappings
• Bifurcation, perturbation of simple eigenvalues, and linearized stability
• Some global results for nonlinear eigenvalue problems
• On the number of solutions of nonlinear equations in ordered Banach spaces
• Uniqueness for sublinear boundary value problems
• Unique and Multiple Solutions of a Family of Differential Equations Modeling Chemical Reactions
• A Comparison of Dispersal Strategies for Survival of Spatially Heterogeneous Populations
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• A Periodicity Threshold Theorem for Some Nonlinear Integral Equations
• Solution branches for mappings in cones, and applications
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