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Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case

Filippakis, Michael E.
; 
O'Regan, Donal
; 
Papageorgiou, Nikolaos S.
Identifiers
http://hdl.handle.net/10379/11466
https://doi.org/10.13025/26904
Repository DOI
10.3934/cpaa.2010.9.1507
Publication Date
2010-08-01
Keywords
p-laplacian, superdiffusive reaction, linking sets, mountain pass theorem, upper-lower solutions, truncation techniques, comparison principle, p-laplace operator, multiple solutions, eigenvalue problems, existence, nonresonance, diffusion, resonance, theorems, sobolev, sign
Type
Article
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Citation
Filippakis, Michael E. O'Regan, Donal; Papageorgiou, Nikolaos S. (2010). Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: the superdiffusive case. Communications on Pure and Applied Analysis 9 (6), 1507-1527
Abstract
We consider a nonlinear elliptic equation of logistic type, driven by the p-Laplacian differential operator with a general superdiffusive reaction. We show that the equation exhibits a bifurcation phenomenon. Namely there is a critical value lambda(*) of the parameter lambda > 0, such that, if lambda > lambda(*), the equation has two nontrivial positive smooth solutions, if lambda = lambda(*), then there is one positive solution and finally if lambda is an element of (0, lambda(*)) then there is no positive solution.
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Publisher
American Institute of Mathematical Sciences (AIMS)
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Attribution-NonCommercial-NoDerivs 3.0 Ireland
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Externally hosted open access publications with University of Galway authors (2)