Open AccessPositive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case
Author(s) -
Michael Ε. Filippakis,
Donal O’Regan,
Nikolaos S. Papageorgiou
Publication year - 2010
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2010.9.1507
Subject(s) - lambda , bifurcation , nonlinear system , mathematical analysis , p laplacian , operator (biology) , laplace operator , physics , type (biology) , mathematical physics , mathematics , elliptic curve , quantum mechanics , boundary value problem , biochemistry , chemistry , repressor , transcription factor , gene , ecology , biology
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