POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

doi:10.1016/S0252-9602(14)60033-3

Acta mathematica scientia,Series B ›› 2014, Vol. 34 ›› Issue (3): 610-618.doi: 10.1016/S0252-9602(14)60033-3

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POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

Leszek GASIÑSKI, Nikolaos S. PAPAGEORGIOU

Jagiellonian University, Faculty of Mathematics and Computer Science, ul. |Lojasiewicza 6, 30-348 Krak´ow, Poland； National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, Greece

Received:2012-09-04 Online:2014-05-20 Published:2014-05-20
Supported by:
The first author is supported by the Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 295118, the National Science Center of Poland under grant No. N N201 604640, the International Project co-financed by the Ministry of Science and Higher Education of Republic of Poland under grant No. W111/7.PR/2012, and the National Science Center of Poland under Maestro Advanced Project No. DEC-2012/06/A/ST1/00262.

Abstract

Abstract:

We consider a parametric Dirichlet problem driven by the p-Laplacian with a Carath´eodory reaction of equidiffusive type. Our hypotheses incorporate as a special case the equidiffusive p-logistic equation. We show that if λ₁ > 0 is the principal eigenvalue of the Dirichlet negative p-Laplacian and λ > λ₁ (λ being the parameter), the problem has a unique positive solution, while for λ ∈(0, λ₁], the problem has no positive solution.

Key words: p-Laplacian, p-logistic equation, first eigenvalue, equidiffusive reaction, maxi-mum principle, nonlinear regularity

CLC Number:

35J25

Leszek GASINSKI, Nikolaos S. PAPAGEORGIOU. POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS[J].Acta mathematica scientia,Series B, 2014, 34(3): 610-618.

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POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS

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