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Volume 36, Issue 2
An Elliptic Nonlinear System of Two Functions with Application

Joon Hyuk Kang & Timothy Robertson

DOI: 10.4208/jpde.v36.n2.2

J. Part. Diff. Eq., 36 (2023), pp. 122-146.

Published online: 2023-07

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  • Abstract

The purpose of this paper is to give a sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain $Ω$ in $R^n.$ Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

  • Keywords

Competition system, coexistence state.

  • AMS Subject Headings

35A05, 35A07

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-36-122, author = {Kang , Joon Hyuk and Robertson , Timothy}, title = {An Elliptic Nonlinear System of Two Functions with Application}, journal = {Journal of Partial Differential Equations}, year = {2023}, volume = {36}, number = {2}, pages = {122--146}, abstract = {

The purpose of this paper is to give a sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain $Ω$ in $R^n.$ Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n2.2}, url = {http://global-sci.org/intro/article_detail/jpde/21838.html} }
TY - JOUR T1 - An Elliptic Nonlinear System of Two Functions with Application AU - Kang , Joon Hyuk AU - Robertson , Timothy JO - Journal of Partial Differential Equations VL - 2 SP - 122 EP - 146 PY - 2023 DA - 2023/07 SN - 36 DO - http://doi.org/10.4208/jpde.v36.n2.2 UR - https://global-sci.org/intro/article_detail/jpde/21838.html KW - Competition system, coexistence state. AB -

The purpose of this paper is to give a sufficient conditions for the existence and uniqueness of positive solutions to a rather general type of elliptic system of the Dirichlet problem on a bounded domain $Ω$ in $R^n.$ Also considered are the effects of perturbations on the coexistence state and uniqueness. The techniques used in this paper are super-sub solutions method, eigenvalues of operators, maximum principles, spectrum estimates, inverse function theory, and general elliptic theory. The arguments also rely on some detailed properties for the solution of logistic equations. These results yield an algebraically computable criterion for the positive coexistence of competing species of animals in many biological models.

Kang , Joon Hyuk and Robertson , Timothy. (2023). An Elliptic Nonlinear System of Two Functions with Application. Journal of Partial Differential Equations. 36 (2). 122-146. doi:10.4208/jpde.v36.n2.2
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