Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth
We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed prob...
| Κύριοι συγγραφείς: | , , |
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| Μορφή: | Άρθρο |
| Γλώσσα: | English |
| Έκδοση: |
University of Szeged
2018-04-01
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| Σειρά: | Electronic Journal of Qualitative Theory of Differential Equations |
| Θέματα: | |
| Διαθέσιμο Online: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6310 |
| _version_ | 1827951187828146176 |
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| author | Nikolaos Papageorgiou Calogero Vetro Francesca Vetro |
| author_facet | Nikolaos Papageorgiou Calogero Vetro Francesca Vetro |
| author_sort | Nikolaos Papageorgiou |
| collection | DOAJ |
| description | We consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution. |
| first_indexed | 2024-04-09T13:37:52Z |
| format | Article |
| id | doaj.art-f981fd9cd7ad4f6883b0bd12ed4c5512 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:52Z |
| publishDate | 2018-04-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f981fd9cd7ad4f6883b0bd12ed4c55122023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-04-012018181910.14232/ejqtde.2018.1.186310Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growthNikolaos Papageorgiou0Calogero Vetro1Francesca Vetro2National Techiniacal University of Athens, GreeceUniversity of Palermo, Palermo, ItalyUniversity of Palermo, Palermo, ItalyWe consider a nonlinear elliptic problem driven by the Dirichlet $p$-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6310convection reaction termnonlinear regularitynonlinear maximum principlepseudomonotone mappicone identityhartman condition |
| spellingShingle | Nikolaos Papageorgiou Calogero Vetro Francesca Vetro Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth Electronic Journal of Qualitative Theory of Differential Equations convection reaction term nonlinear regularity nonlinear maximum principle pseudomonotone map picone identity hartman condition |
| title | Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth |
| title_full | Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth |
| title_fullStr | Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth |
| title_full_unstemmed | Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth |
| title_short | Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth |
| title_sort | existence of positive solutions for nonlinear dirichlet problems with gradient dependence and arbitrary growth |
| topic | convection reaction term nonlinear regularity nonlinear maximum principle pseudomonotone map picone identity hartman condition |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6310 |
| work_keys_str_mv | AT nikolaospapageorgiou existenceofpositivesolutionsfornonlineardirichletproblemswithgradientdependenceandarbitrarygrowth AT calogerovetro existenceofpositivesolutionsfornonlineardirichletproblemswithgradientdependenceandarbitrarygrowth AT francescavetro existenceofpositivesolutionsfornonlineardirichletproblemswithgradientdependenceandarbitrarygrowth |