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1995 On the spectrum of some linear noncooperative elliptic systems with radial symmetry
E. N. Dancer, J. López-Gómez, R. Ortega
Differential Integral Equations 8(3): 515-523 (1995).

Abstract

In this work we study the spectrum of some linear weakly coupled noncooperative elliptic systems with two species subject to homogeneous Dirichlet boundary conditions. When the domain supporting the species is a ball or an annulus we prove that zero is never an eigenvalue. As a consequence of this result we also show that the classical Lotka-Volterra predator-prey model with diffusion and radial function coefficients has a unique component-wise radial coexistence state with no zero eigenvalue of the linearization on the space $W^{2,p}(D)$, $p > {N\over 2}$. Therefore, a radially symmetric coexistence state only may lose stability by a Hopf bifurcation when we vary parameters.

Citation

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E. N. Dancer. J. López-Gómez. R. Ortega. "On the spectrum of some linear noncooperative elliptic systems with radial symmetry." Differential Integral Equations 8 (3) 515 - 523, 1995.

Information

Published: 1995
First available in Project Euclid: 23 May 2013

zbMATH: 0841.35031
MathSciNet: MR1306571

Subjects:
Primary: 35J25
Secondary: 35B32, 35P05, 92D25, 92D40

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 3 • 1995
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