Positive solutions for Robin problems with general potential and logistic reaction

Shouchuan Hu; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2016046

Article Contents

2016, Volume 15, Issue 6: 2489-2507. Doi: 10.3934/cpaa.2016046

This issue Previous Article Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains Next Article On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line

Positive solutions for Robin problems with general potential and logistic reaction

Shouchuan Hu^1, and
Nikolaos S. Papageorgiou^2,

1.
Department of Mathematics, Missouri State University, Springeld, MO 65804
2.
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780

Received: January 31, 2016

Revised: July 31, 2016

Published: October 2016

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Abstract

We consider a semilinear Robin problem driven by the negative Laplacian plus an indefinite and unbounded potential and a superdiffusive lotistic-type reaction. We prove bifurcation results describing the dependence of the set of positive solutions on the parameter of the problem. We also establish the existence of extreme positive solutions and determine their properties.

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Mathematics Subject Classification: 35J20, 35J60, 58E05.

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