A variational approach to nonlinear logistic equations

Leszek Gasiński; Donal O'Regan; Nikolaos S. Papageorgiou

doi:10.1142/S0219199714500217

A variational approach to nonlinear logistic equations

Leszek Gasiński
, Donal O'Regan
, Nikolaos S. Papageorgiou

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

23 Citations (Scopus)

Abstract

We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of constant sign and in fact we establish the existence of extremal constant sign solutions. Using these extremal solutions, we produce a nodal (sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

Original language	English
Article number	1450021
Journal	Communications in Contemporary Mathematics
Volume	17
Issue number	3
DOIs	https://doi.org/10.1142/S0219199714500217
Publication status	Published - 25 Jun 2015

Keywords

Nonlinear logistic equation
degenerate logistic equation
maximum principle
nonlinear regularity theory
positive solution

Authors (Note for portal: view the doc link for the full list of authors)

Authors
Gasinski, L,O'Regan, D,Papageorgiou, NS

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10.1142/S0219199714500217

Cite this

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title = "A variational approach to nonlinear logistic equations",

abstract = "We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of constant sign and in fact we establish the existence of extremal constant sign solutions. Using these extremal solutions, we produce a nodal (sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.",

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AU - Papageorgiou, Nikolaos S.

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Y1 - 2015/6/25

N2 - We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of constant sign and in fact we establish the existence of extremal constant sign solutions. Using these extremal solutions, we produce a nodal (sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

AB - We consider a nonlinear logistic type equation. For all big values of the parameter, we show that the problem admits nontrivial solutions of constant sign and in fact we establish the existence of extremal constant sign solutions. Using these extremal solutions, we produce a nodal (sign-changing) solution. We also investigate the uniqueness and continuous dependence on the parameter of positive solutions. Finally, we study the degenerate p-logistic equation.

KW - Nonlinear logistic equation

KW - degenerate logistic equation

KW - maximum principle

KW - nonlinear regularity theory

KW - positive solution

UR - https://www.scopus.com/pages/publications/84928588914

U2 - 10.1142/S0219199714500217

DO - 10.1142/S0219199714500217

M3 - Article

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VL - 17

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 3

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ER -

A variational approach to nonlinear logistic equations

Abstract

Keywords

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