On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus
The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general $\phi $-Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2022-09-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9859 |
| _version_ | 1827951106341208064 |
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| author | Jorge Rodríguez-López Radu Precup Calin-Ioan Gheorghiu |
| author_facet | Jorge Rodríguez-López Radu Precup Calin-Ioan Gheorghiu |
| author_sort | Jorge Rodríguez-López |
| collection | DOAJ |
| description | The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general $\phi $-Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun. |
| first_indexed | 2024-04-09T13:36:28Z |
| format | Article |
| id | doaj.art-bd6c1acf59ea4c38b2fb7aaedb2b4ab8 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:28Z |
| publishDate | 2022-09-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-bd6c1acf59ea4c38b2fb7aaedb2b4ab82023-05-09T07:53:12ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752022-09-0120224712210.14232/ejqtde.2022.1.479859On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulusJorge Rodríguez-López0Radu Precup1Calin-Ioan Gheorghiu2Universidade de Santiago de Compostela, Santiago de Compostela, SpainMathematics, Universitatea Babes-Bolyai, Cluj-Napoca, RomaniaTiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, RomaniaThe paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general $\phi $-Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The results are based on the homotopy version of Krasnosel'skii's fixed point theorem and Harnack type inequalities, first established for each one of the boundary conditions. As a consequence, the problem of multiple solutions is solved in a natural way. Numerical experiments confirming the theory, one for each of the three sets of boundary conditions, are performed by using the MATLAB object-oriented package Chebfun.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9859$\phi $-laplace operatorradial solutionpositive solutionfixed point indexharnack type inequalitynumerical solution |
| spellingShingle | Jorge Rodríguez-López Radu Precup Calin-Ioan Gheorghiu On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus Electronic Journal of Qualitative Theory of Differential Equations $\phi $-laplace operator radial solution positive solution fixed point index harnack type inequality numerical solution |
| title | On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus |
| title_full | On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus |
| title_fullStr | On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus |
| title_full_unstemmed | On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus |
| title_short | On the localization and numerical computation of positive radial solutions for $\phi $-Laplace equations in the annulus |
| title_sort | on the localization and numerical computation of positive radial solutions for phi laplace equations in the annulus |
| topic | $\phi $-laplace operator radial solution positive solution fixed point index harnack type inequality numerical solution |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=9859 |
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