Positive solutions for nonlinear nonhomogeneous robin problems

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

doi:10.4171/ZAA/1548

Positive solutions for nonlinear nonhomogeneous robin problems

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

Mathematics

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8 Citations (Scopus)

Abstract

We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near 0⁺ and near +∞: We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.

Original language	English
Pages (from-to)	435-458
Number of pages	24
Journal	Zeitschrift für Analysis und ihre Anwendungen
Volume	34
Issue number	4
DOIs	https://doi.org/10.4171/ZAA/1548
Publication status	Published - 1 Jan 2015

Keywords

Logistic equations
Nonlinear maximum principle
Nonlinear regularity
Positive solution
Smallest 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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10.4171/ZAA/1548

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abstract = "We consider a nonlinear, nonhomogeneous Robin problem with a Carath{\'e}odory reaction which satisfies certain general growth conditions near 0+ and near +∞: We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.",

keywords = "Logistic equations, Nonlinear maximum principle, Nonlinear regularity, Positive solution, Smallest positive solution",

author = "Leszek Gasi{\'n}ski and Donal O'Regan and Papageorgiou, \{Nikolaos S.\}",

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AU - O'Regan, Donal

AU - Papageorgiou, Nikolaos S.

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near 0+ and near +∞: We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.

AB - We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfies certain general growth conditions near 0+ and near +∞: We show the existence and regularity of positive solutions, the existence of a smallest positive solution and under an additional condition on the reaction, we show the uniqueness of the positive solutions. We then show that our setting incorporates certain parametric Robin equations of interest such as nonlinear equidiffusive logistic equations.

KW - Logistic equations

KW - Nonlinear maximum principle

KW - Nonlinear regularity

KW - Positive solution

KW - Smallest positive solution

UR - https://www.scopus.com/pages/publications/84944326791

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DO - 10.4171/ZAA/1548

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VL - 34

SP - 435

EP - 458

JO - Zeitschrift für Analysis und ihre Anwendungen

JF - Zeitschrift für Analysis und ihre Anwendungen

IS - 4

ER -

Positive solutions for nonlinear nonhomogeneous robin problems

Abstract

Keywords

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