Acta mathematica scientia, Series B >
POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS
Received date: 2012-09-04
Online 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.
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.
Leszek GASINSKI , Nikolaos S. PAPAGEORGIOU . POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS[J]. Acta mathematica scientia, Series B, 2014 , 34(3) : 610 -618 . DOI: 10.1016/S0252-9602(14)60033-3
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