Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions
We consider the following class of nonlinear singular differential equation −(𝑝(𝑥)𝑦′(𝑥))′+𝑞(𝑥)𝑓(𝑥,𝑦(𝑥),𝑝(𝑥)𝑦′(𝑥))=0,0<𝑥<1 subject to the Neumann boundary condition 𝑦′(0)=𝑦′(1)=0. Conditions on 𝑝(𝑥) and 𝑞(𝑥) ensure that 𝑥=0 is a singular point of limit circle type. A simple approximation scheme...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2011/986948 |
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| author | Amit K. Verma Lajja Verma |
| author_facet | Amit K. Verma Lajja Verma |
| author_sort | Amit K. Verma |
| collection | DOAJ |
| description | We consider the following class of nonlinear singular differential equation −(𝑝(𝑥)𝑦′(𝑥))′+𝑞(𝑥)𝑓(𝑥,𝑦(𝑥),𝑝(𝑥)𝑦′(𝑥))=0,0<𝑥<1 subject to the Neumann boundary condition 𝑦′(0)=𝑦′(1)=0. Conditions on 𝑝(𝑥) and 𝑞(𝑥) ensure that 𝑥=0 is a singular point of limit circle type. A simple approximation scheme which is iterative in nature is considered. The initial iterates are upper and lower solutions which can be ordered in one way (𝑣0≤𝑢0) or the other (𝑢0≤𝑣0). |
| format | Article |
| id | doaj-art-bc1c6bc585f84ee0aaa8bb2d4193660f |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-bc1c6bc585f84ee0aaa8bb2d4193660f2025-02-03T06:42:17ZengWileyInternational Journal of Differential Equations1687-96431687-96512011-01-01201110.1155/2011/986948986948Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower SolutionsAmit K. Verma0Lajja Verma1Department of Mathematics, BITS Pilani, Pilani, Rajasthan 333031, IndiaDepartment of Mathematics and Astronomy, University of Lucknow, Lucknow 226007, IndiaWe consider the following class of nonlinear singular differential equation −(𝑝(𝑥)𝑦′(𝑥))′+𝑞(𝑥)𝑓(𝑥,𝑦(𝑥),𝑝(𝑥)𝑦′(𝑥))=0,0<𝑥<1 subject to the Neumann boundary condition 𝑦′(0)=𝑦′(1)=0. Conditions on 𝑝(𝑥) and 𝑞(𝑥) ensure that 𝑥=0 is a singular point of limit circle type. A simple approximation scheme which is iterative in nature is considered. The initial iterates are upper and lower solutions which can be ordered in one way (𝑣0≤𝑢0) or the other (𝑢0≤𝑣0).http://dx.doi.org/10.1155/2011/986948 |
| spellingShingle | Amit K. Verma Lajja Verma Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions International Journal of Differential Equations |
| title | Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions |
| title_full | Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions |
| title_fullStr | Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions |
| title_full_unstemmed | Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions |
| title_short | Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions |
| title_sort | nonlinear singular bvp of limit circle type and the presence of reverse ordered upper and lower solutions |
| url | http://dx.doi.org/10.1155/2011/986948 |
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