Positive solutions and bifurcation phenomena for nonlinear elliptic equations of logistic type: The superdiffusive case | Zendy

Michael Ε. Filippakis | Zendy; Donal O’Regan | Zendy; Nikolaos S. Papageorgiou | Zendy

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Positive 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 andamp 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

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