Decaying positive global solutions of second order difference equations with mean curvature operator
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866913797509218304 |
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| author | Došlá, Zuzana Matucci, Serena Řehák, Pavel |
| author_facet | Došlá, Zuzana Matucci, Serena Řehák, Pavel |
| contents | A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is examined by proving new Sturm comparison theorems for linear difference equations and using a fixed point approach based on a linearization device. %The process from the continuous problem to discrete one is examined, too. The process of discretization of the boundary value problem on the unbounded domain is examined, and some discrepancies between the discrete and the continuous case are pointed out, too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_12048 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Decaying positive global solutions of second order difference equations with mean curvature operator Došlá, Zuzana Matucci, Serena Řehák, Pavel Classical Analysis and ODEs 39A22, 39A05, 39A12 A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is examined by proving new Sturm comparison theorems for linear difference equations and using a fixed point approach based on a linearization device. %The process from the continuous problem to discrete one is examined, too. The process of discretization of the boundary value problem on the unbounded domain is examined, and some discrepancies between the discrete and the continuous case are pointed out, too. |
| title | Decaying positive global solutions of second order difference equations with mean curvature operator |
| topic | Classical Analysis and ODEs 39A22, 39A05, 39A12 |
| url | https://arxiv.org/abs/2011.12048 |