<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We extend Theorem 1.1 of [J. Math. Anal. Appl. <bold>435</bold> (2016), 1738-1752] to show the uniqueness of large solutions for the system of (<xref ref-type="disp-formula" rid="j_AMNS.2017.1.00021_equ_001_w2aab3b7e1254b1b6b1ab1ab3aAa">1</xref>) in star-shaped domains. This result is due to the maximum principle for cooperative systems of [J. López-Gómez and M. Molina-Meyer, Diff. Int. Eq. <bold>7</bold> (1994), 383-398], which allows us to establish the uniqueness without invoking to the blow-up rates of the solutions.</p></abstract>

We extend Theorem 1.1 of [J. Math. Anal. Appl. 435 (2016), 1738-1752] to show the uniqueness of large solutions for the system of (1) in star-shaped domains. This result is due to the maximum principle for cooperative systems of [J. López-Gómez and M. Molina-Meyer, Diff. Int. Eq. 7 (1994), 383-398], which allows us to establish the uniqueness without invoking to the blow-up rates of the solutions.

Large solutions for cooperative logistic systems: existence and uniqueness in star-shaped domains

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

We extend Theorem 1.1 of [J. Math. Anal. Appl. 435 (2016), 1738-1752] to show the uniqueness of large solutions for the system of (1) in star-shaped domains....

Large solutions for cooperative logistic systems: existence and uniqueness in star-shaped domains

Published Online: Jun 26, 2017

Page range: 249 - 258

Received: Mar 22, 2017

Accepted: Jun 26, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00021

Keywords
Large positive solution, Cooperative system, Logistic equation, Uniqueness, Keller-Osserman

© 2017 Luis Maire, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Large solutions for cooperative logistic systems: existence and uniqueness in star-shaped domains

Published Online: Jun 26, 2017

Page range: 249 - 258

Received: Mar 22, 2017

Accepted: Jun 26, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00021

KeywordsLarge positive solution, Cooperative system, Logistic equation, Uniqueness, Keller-Osserman

© 2017 Luis Maire, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Large positive solution, Cooperative system, Logistic equation, Uniqueness, Keller-Osserman