On a Robin (p,q)-equation with a logistic reaction
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in...
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AGH Univeristy of Science and Technology Press
2019-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol39/2/art/opuscula_math_3915.pdf |
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doaj-3ddb0f573f2b4848a7091b81f2290cdb2020-11-25T00:32:14ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742019-01-01392227245https://doi.org/10.7494/OpMath.2019.39.2.2273915On a Robin (p,q)-equation with a logistic reactionNikolaos S. Papageorgiou0Calogero Vetro1https://orcid.org/0000-0001-5836-6847Francesca Vetro2https://orcid.org/0000-0001-7448-5299National Technical University, Department of Mathematics, Zografou Campus, 15780, Athens, GreeceUniversity of Palermo, Department of Mathematics and Computer Science, Via Archirafi 34, 90123, Palermo, ItalyNonlinear Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, VietnamWe consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.https://www.opuscula.agh.edu.pl/vol39/2/art/opuscula_math_3915.pdfpositive solutionssuperdiffusive reactionlocal minimizersmaximum principleminimal positive solutionsrobin boundary conditionindefinite potential |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Nikolaos S. Papageorgiou Calogero Vetro Francesca Vetro |
| spellingShingle |
Nikolaos S. Papageorgiou Calogero Vetro Francesca Vetro On a Robin (p,q)-equation with a logistic reaction Opuscula Mathematica positive solutions superdiffusive reaction local minimizers maximum principle minimal positive solutions robin boundary condition indefinite potential |
| author_facet |
Nikolaos S. Papageorgiou Calogero Vetro Francesca Vetro |
| author_sort |
Nikolaos S. Papageorgiou |
| title |
On a Robin (p,q)-equation with a logistic reaction |
| title_short |
On a Robin (p,q)-equation with a logistic reaction |
| title_full |
On a Robin (p,q)-equation with a logistic reaction |
| title_fullStr |
On a Robin (p,q)-equation with a logistic reaction |
| title_full_unstemmed |
On a Robin (p,q)-equation with a logistic reaction |
| title_sort |
on a robin (p,q)-equation with a logistic reaction |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2019-01-01 |
| description |
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution. |
| topic |
positive solutions superdiffusive reaction local minimizers maximum principle minimal positive solutions robin boundary condition indefinite potential |
| url |
https://www.opuscula.agh.edu.pl/vol39/2/art/opuscula_math_3915.pdf |
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AT nikolaosspapageorgiou onarobinpqequationwithalogisticreaction AT calogerovetro onarobinpqequationwithalogisticreaction AT francescavetro onarobinpqequationwithalogisticreaction |
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