Maximum Principles and Principal Eigenvalues

Amann, Herbert

doi:10.1016/b978-044451861-3/50001-x

Cited by 28 publications

(65 citation statements)

References 48 publications

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“…according to [2,Theorem 16] and so 0 belongs to the resolvent set of the operator −Δ D + r − η + 2α 1 U η . We define R :…”

Section: Bifurcation For the Parameter ξmentioning

confidence: 99%

Coexistence steady states in a predator–prey model

Walker

2010

Arch. Math.

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An age-structured predator-prey system with diffusion and Holling-Tanner-type nonlinearities is investigated. Regarding the intensity of the fertility of the predator as bifurcation parameter, we prove that a branch of positive coexistence steady states bifurcates from the marginal steady state with no predator. A similar result is shown when the fertility of the prey varies. Mathematics Subject Classification (2000). 35K55, 35K90, 92D25.

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“…according to [2,Theorem 16] and so 0 belongs to the resolvent set of the operator −Δ D + r − η + 2α 1 U η . We define R :…”

Section: Bifurcation For the Parameter ξmentioning

confidence: 99%

Coexistence steady states in a predator–prey model

Walker

2010

Arch. Math.

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“…The basic ideas of this approach where suggested in the papers of H.Aman and D.Sattinger (see [2,3]) and recently got a father development in the works of P. Hess [4] and H.Aman [5]. These works are essentially using so called Krein-Ruthman theorem ( see, for example, [4]) and basic results of M.A.…”

Section: Introductionmentioning

confidence: 98%

Comparison Principle for Reaction-Diffusion-Advection Problems with Boundary and Internal Layers

Нефедов

2013

Lecture Notes in Computer Science

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Abstract. In the present paper we discuss father development of the general scheme of the asymptotic method of differential inequalities and illustrate it applying for some new important cases of initial boundary value problem for the nonlinear singularly perturbed parabolic equations,which are called in applications as reaction-diffusion-advection equations. The theorems which state front motion description and stationary contrast structures formation are proved for parabolic, parabolic-periodic and integro-parabolic problems.

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“…Eigenvalue problems have been studied extensively by several researchers, but we refer the reader to [1][2][3][4] and the references therein. For further details of eigenvalue problems that involve the p-Laplacian operator, the reader may refer to [5][6][7] and the references therein.…”

Section: Introductionmentioning

confidence: 99%