On the localization and numerical computation of positive radial solutions for ϕ-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 ϕ-Laplace operator in the annulus. Three sets of boundary conditions are considered: Dirichlet–Neumann, Neumann–Dirichlet and Dirichlet–Dirichlet. The re...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | ϕ-Laplace operátor, Harnack típusú egyenlőtlenség, Laplace-egyenlet |
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| doi: | 10.14232/ejqtde.2022.1.47 |
| Online Access: | http://acta.bibl.u-szeged.hu/78332 |
| Tartalmi kivonat: | The paper deals with the existence and localization of positive radial solutions for stationary partial differential equations involving a general ϕ-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’ski˘ı’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. |
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| ISSN: | 1417-3875 |