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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.
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.
Keyword(s): 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
Publication Date:
2018
Type: Journal article
Peer-Reviewed: Unknown
Institution: NUI Galway
Publisher(s): American Institute of Mathematical Sciences (AIMS)
First Indexed: 2019-03-23 06:24:12 Last Updated: 2019-03-23 06:24:12