American Institute of Mathematical Sciences

Advanced
October  1996, 2(4): 525-542. doi: 10.3934/dcds.1996.2.525

On the structure of the permanence region for competing species models with general diffusivities and transport effects

Julián López-Gómez 1,

1. 

Departamento de Matemática Aplicada, Universidad Complutense, 28040-MADRID, Spain

Received  October 1995 Revised  March 1996 Published  July 1996

In this work we study the problem of the coexistence of two competing species in an inhabited region by analyzing the shape of the region where the species exhibit permanence. To make this analysis we first obtain a singular perturbation result for an elliptic boundary value problem associated to a logistic equation with a general differential operator. Then, we analyze how varies the principal eigenvalue of the operator at its singular limit in the case when the operator admits a reduction to the selfadjoint case. These results are new and of a great interest by themselves. Finally, we shall apply them to the problem of the permanence.
Keywords: elliptic boundary value problem, principal eigenvalue..
Mathematics Subject Classification: 35K50, 35K57, 35B4.
Citation: Julián López-Gómez. On the structure of the permanence region for competing species models with general diffusivities and transport effects. Discrete & Continuous Dynamical Systems, 1996, 2 (4) : 525-542. doi: 10.3934/dcds.1996.2.525
[1]

J. R. L. Webb. Uniqueness of the principal eigenvalue in nonlocal boundary value problems. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 177-186. doi: 10.3934/dcdss.2008.1.177
[2]

Chiu-Yen Kao, Yuan Lou, Eiji Yanagida. Principal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains. Mathematical Biosciences & Engineering, 2008, 5 (2) : 315-335. doi: 10.3934/mbe.2008.5.315
[3]

Pablo Blanc. A lower bound for the principal eigenvalue of fully nonlinear elliptic operators. Communications on Pure & Applied Analysis, 2020, 19 (7) : 3613-3623. doi: 10.3934/cpaa.2020158
[4]

Bastian Gebauer, Nuutti Hyvönen. Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem. Inverse Problems & Imaging, 2008, 2 (3) : 355-372. doi: 10.3934/ipi.2008.2.355
[5]

Angelo Favini, Rabah Labbas, Stéphane Maingot, Maëlis Meisner. Boundary value problem for elliptic differential equations in non-commutative cases. Discrete & Continuous Dynamical Systems, 2013, 33 (11&12) : 4967-4990. doi: 10.3934/dcds.2013.33.4967
[6]

VicenŢiu D. RǍdulescu, Somayeh Saiedinezhad. A nonlinear eigenvalue problem with $ p(x) $-growth and generalized Robin boundary value condition. Communications on Pure & Applied Analysis, 2018, 17 (1) : 39-52. doi: 10.3934/cpaa.2018003
[7]

Lisa Hollman, P. J. McKenna. A conjecture on multiple solutions of a nonlinear elliptic boundary value problem: some numerical evidence. Communications on Pure & Applied Analysis, 2011, 10 (2) : 785-802. doi: 10.3934/cpaa.2011.10.785
[8]

Paolo Piersanti. On the improved interior regularity of a boundary value problem modelling the displacement of a linearly elastic elliptic membrane shell subject to an obstacle. Discrete & Continuous Dynamical Systems, 2022, 42 (2) : 1011-1037. doi: 10.3934/dcds.2021145
[9]

Sunghan Kim, Ki-Ahm Lee, Henrik Shahgholian. Homogenization of the boundary value for the Dirichlet problem. Discrete & Continuous Dynamical Systems, 2019, 39 (12) : 6843-6864. doi: 10.3934/dcds.2019234
[10]

Hugo Beirão da Veiga. Elliptic boundary value problems in spaces of continuous functions. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 43-52. doi: 10.3934/dcdss.2016.9.43
[11]

Fei-Ying Yang, Wan-Tong Li, Jian-Wen Sun. Principal eigenvalues for some nonlocal eigenvalue problems and applications. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 4027-4049. doi: 10.3934/dcds.2016.36.4027
[12]

Getachew K. Befekadu, Panos J. Antsaklis. On noncooperative $n$-player principal eigenvalue games. Journal of Dynamics & Games, 2015, 2 (1) : 51-63. doi: 10.3934/jdg.2015.2.51
[13]

Aixia Qian, Shujie Li. Multiple sign-changing solutions of an elliptic eigenvalue problem. Discrete & Continuous Dynamical Systems, 2005, 12 (4) : 737-746. doi: 10.3934/dcds.2005.12.737
[14]

Vladimir V. Varlamov. On the initial boundary value problem for the damped Boussinesq equation. Discrete & Continuous Dynamical Systems, 1998, 4 (3) : 431-444. doi: 10.3934/dcds.1998.4.431
[15]

Mauro Garavello. Boundary value problem for a phase transition model. Networks & Heterogeneous Media, 2016, 11 (1) : 89-105. doi: 10.3934/nhm.2016.11.89
[16]

Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla. Positive radial solutions of a nonlinear boundary value problem. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1765-1783. doi: 10.3934/cpaa.2018084
[17]

Marta García-Huidobro, Raul Manásevich. A three point boundary value problem containing the operator. Conference Publications, 2003, 2003 (Special) : 313-319. doi: 10.3934/proc.2003.2003.313
[18]

Gen Nakamura, Michiyuki Watanabe. An inverse boundary value problem for a nonlinear wave equation. Inverse Problems & Imaging, 2008, 2 (1) : 121-131. doi: 10.3934/ipi.2008.2.121
[19]

Yuebin Hao. Electromagnetic interior transmission eigenvalue problem for an inhomogeneous medium with a conductive boundary. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1387-1397. doi: 10.3934/cpaa.2020068
[20]

Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615

2020 Impact Factor: 1.392

Tools

Metrics

  • PDF downloads (69)
  • HTML views (0)
  • Cited by (15)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy