Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions

Amit K. Verma and Lajja Verma

International Journal of Differential Equations, 2011, vol. 2011, 1-13

Abstract:

We consider the following class of nonlinear singular differential equation − ( ð ‘ ( ð ‘¥ ) 𠑦 ′ ( ð ‘¥ ) ) ′ + ð ‘ž ( ð ‘¥ ) ð ‘“ ( ð ‘¥ , 𠑦 ( ð ‘¥ ) , ð ‘ ( ð ‘¥ ) 𠑦 ′ ( ð ‘¥ ) ) = 0 , 0 < ð ‘¥ < 1 subject to the Neumann boundary condition 𠑦 ′ ( 0 ) = 𠑦 ′ ( 1 ) = 0 . Conditions on ð ‘ ( ð ‘¥ ) and ð ‘ž ( ð ‘¥ ) ensure that ð ‘¥ = 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 ( ð ‘£ 0 ≤ ð ‘¢ 0 ) or the other ( ð ‘¢ 0 ≤ ð ‘£ 0 ) .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:986948

DOI: 10.1155/2011/986948

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