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 pLaplacian 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 &gt; 0, such that, if lambda &gt; 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):

plaplacian; superdiffusive reaction; linking sets; mountain pass theorem; upperlower solutions; truncation techniques; comparison principle; plaplace operator; multiple solutions; eigenvalue problems; existence; nonresonance; diffusion; resonance; theorems; sobolev; sign 
Publication Date:

2018 
Type:

Journal article 
PeerReviewed:

Unknown 
Institution:

NUI Galway 
Publisher(s):

American Institute of Mathematical Sciences (AIMS) 
First Indexed:
20190323 06:24:12 Last Updated:
20190323 06:24:12 