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Zeitschrift für Analysis und ihre Anwendungen

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Volume 34, Issue 4, 2015, pp. 435–458
DOI: 10.4171/ZAA/1548

Published online: 2015-10-29

Positive Solutions for Nonlinear Nonhomogeneous Robin Problems

Leszek Gasiński[1], Donal O'Regan[2] and Nikolaos S. Papageorgiou[3]

(1) Jagiellonian University, Kraków, Poland
(2) National University of Ireland, Galway, Ireland
(3) National Technical University of Athens, Greece

We consider a nonlinear, nonhomogeneous Robin problem with a Carathéodory reaction which satisfi es certain general growth conditions near $0^+$ and near $+ \infty$. 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 equidi ffusive logistic equations.

Keywords: Positive solution, nonlinear regularity, nonlinear maximum principle, logistic equations, smallest positive solution

Gasiński Leszek, O'Regan Donal, Papageorgiou Nikolaos: Positive Solutions for Nonlinear Nonhomogeneous Robin Problems. Z. Anal. Anwend. 34 (2015), 435-458. doi: 10.4171/ZAA/1548