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On a nonlinear elliptic eigenvalue problem with Neumann boundary conditions, with an application to population genetics
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In this paper, a nonlinear elliptic eigenvalue problem with neumann boundary conditions, with an application to population genetics, is studied. But the authors focus on population genetics only.Abstract:
(1983). On a nonlinear elliptic eigenvalue problem with neumann boundary conditions, with an application to population genetics. Communications in Partial Differential Equations: Vol. 8, No. 11, pp. 1199-1228.read more
Citations
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On the Dynamics of Predator–Prey Models with the Beddington–DeAngelis Functional Response☆
TL;DR: In this article, the dynamics of predator-prey models with the Beddington-DeAngelis functional response were analyzed from the viewpoint of permanence and extinction, and criteria for permanence were derived for systems without diffusion or with no-flux boundary conditions.
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Analysis of the periodically fragmented environment model: I--species persistence.
TL;DR: The existence and uniqueness results for the stationary equation are proved and the behaviour of the solutions of the evolution equation for large times is analyzed.
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Movement toward better environments and the evolution of rapid diffusion.
TL;DR: Under suitable conditions on the underlying spatial domain, the competitor that moves toward more favorable environments may have a competitive advantage even if it diffuses more rapidly than the other competitor, in contrast with the case in which both competitors disperse by pure diffusion.
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On the effects of spatial heterogeneity on the persistence of interacting species
TL;DR: In this article, the authors model the dynamics of two interacting theoretical populations inhabiting a heterogeneous environment by a system of two weakly coupled reaction-diffusion equations having spatially dependent reaction terms.
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Minimization of the Principal Eigenvalue for an Elliptic Boundary Value Problem with Indefinite Weight, and Applications to Population Dynamics
Yuan Lou,Eiji Yanagida +1 more
TL;DR: In this article, it was shown that every global minimizer must be of "bang-bang" type and that there are exactly two global minimizers for which the weight is positive at one end of the interval and is negative in the remainder.
References
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Bifurcation from simple eigenvalues
TL;DR: In this article, a general version of the main problem of bifurcation theory, given p ϵ C, determine the structure of G−1{0} in some neighborhood of p.
Journal ArticleDOI
Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
TL;DR: A survey of nonlinear functional analysis in ordered Banach spaces can be found in this paper, where some of the most important methods and results of non-linear functional analyses are discussed.
Journal ArticleDOI
Some global results for nonlinear eigenvalue problems
TL;DR: In this paper, the structure of the solution set for a large class of nonlinear eigenvalue problems in a Banach space is investigated, and the existence of continua, i.e., closed connected sets, of solutions of these equations is demonstrated.
Book
Topics in Nonlinear Functional Analysis
TL;DR: Topological approach: Finite dimensions Topological degree in Banach space Bifurcation theory Further topological methods Monotone operators and the min-max theorem Generalized implicit function theorems Bibliography as mentioned in this paper
Journal ArticleDOI
Bifurcation, perturbation of simple eigenvalues, itand linearized stability
TL;DR: In this article, the eigenvalue of minimum modulus of the Frechet derivative of a nonlinear operator is estimated along a bifurcating curve of zeros of the operator.
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