Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term
We consider a nonlinear Robin problem driven by the anisotropic $(p,q)$-Laplacian plus an indefinite potential term. In the reaction, we have the competing effects of a parametric concave (sublinear) term perturbed by a superlinear one (concave-convex problem). We prove the existence and multiplicit...
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University of Szeged
2024-10-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11100 |
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| _version_ | 1841533477890031616 |
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| author | Eylem Öztürk Nikolaos Papageorgiou |
| author_facet | Eylem Öztürk Nikolaos Papageorgiou |
| author_sort | Eylem Öztürk |
| collection | DOAJ |
| description | We consider a nonlinear Robin problem driven by the anisotropic $(p,q)$-Laplacian plus an indefinite potential term. In the reaction, we have the competing effects of a parametric concave (sublinear) term perturbed by a superlinear one (concave-convex problem). We prove the existence and multiplicity result for positive solutions which is global with respect to the parameter. We also show the existence of a minimal positive solution and determine its dependence on the parameter. |
| format | Article |
| id | doaj-art-41850da0d638472cbb8345ab5a512982 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-41850da0d638472cbb8345ab5a5129822025-01-15T21:24:59ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-10-0120245812510.14232/ejqtde.2024.1.5811100Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential termEylem Öztürk0https://orcid.org/0000-0002-0636-3430Nikolaos Papageorgiouhttps://orcid.org/0000-0003-4800-1187Hacettepe University, Beytepe, Ankara, TurkeyWe consider a nonlinear Robin problem driven by the anisotropic $(p,q)$-Laplacian plus an indefinite potential term. In the reaction, we have the competing effects of a parametric concave (sublinear) term perturbed by a superlinear one (concave-convex problem). We prove the existence and multiplicity result for positive solutions which is global with respect to the parameter. We also show the existence of a minimal positive solution and determine its dependence on the parameter.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11100nonlinear nonhomogeneous differential operatorindefinite potentialpositive solutionstruncations and comparisonsnonlinear regularity$(pq)$-laplacianrobin boundary |
| spellingShingle | Eylem Öztürk Nikolaos Papageorgiou Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term Electronic Journal of Qualitative Theory of Differential Equations nonlinear nonhomogeneous differential operator indefinite potential positive solutions truncations and comparisons nonlinear regularity $(p q)$-laplacian robin boundary |
| title | Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term |
| title_full | Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term |
| title_fullStr | Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term |
| title_full_unstemmed | Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term |
| title_short | Global multiplicity of positive solutions for anisotropic $(p,q)$-Robin boundary value problems with an indefinite potential term |
| title_sort | global multiplicity of positive solutions for anisotropic p q robin boundary value problems with an indefinite potential term |
| topic | nonlinear nonhomogeneous differential operator indefinite potential positive solutions truncations and comparisons nonlinear regularity $(p q)$-laplacian robin boundary |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=11100 |
| work_keys_str_mv | AT eylemozturk globalmultiplicityofpositivesolutionsforanisotropicpqrobinboundaryvalueproblemswithanindefinitepotentialterm AT nikolaospapageorgiou globalmultiplicityofpositivesolutionsforanisotropicpqrobinboundaryvalueproblemswithanindefinitepotentialterm |