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Positive Solutions for the Generalized Nonlinear Logistic Equations

Published online by Cambridge University Press:  20 November 2018

Leszek Gasiński and
Nikolaos S. Papageorgiou
Leszek Gasiński
Affiliation:
Jagiellonian University, Faculty of Mathematics and Computer Science, Kraków, Poland e-mail: leszek.gasinski@ii.uj.edu.pl
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece e-mail: npapg@math.ntua.gr
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Abstract

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We consider a nonlinear parametric elliptic equation driven by a nonhomogeneous differential operator with a logistic reaction of the superdiffusive type. Using variational methods coupled with suitable truncation and comparison techniques, we prove a bifurcation type result describing the set of positive solutions as the parameter varies.

Keywords

35J2535J92positive solutionbifurcation type resultstrong comparison principlenonlinear regularitynonlinear maximum principle

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016, pp. 73 - 86
Copyright
Copyright © Canadian Mathematical Society 2016

References

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