Multiple Solutions for Nonlinear Doubly Singular Three-Point Boundary Value Problems with Derivative Dependence

R. K. Pandey and A. K. Barnwal

International Journal of Differential Equations, 2012, vol. 2012, 1-21

Abstract:

We study the existence of multiple nonnegative solutions for the doubly singular three-point boundary value problem with derivative dependent data function − ( ð ‘ ( ð ‘¡ ) 𠑦 ′ ( ð ‘¡ ) ) ′ = ð ‘ž ( ð ‘¡ ) ð ‘“ ( ð ‘¡ , 𠑦 ( ð ‘¡ ) , ð ‘ ( ð ‘¡ ) 𠑦 ′ ( ð ‘¡ ) ) , 0 < ð ‘¡ < 1 , 𠑦 ( 0 ) = 0 , 𠑦 ( 1 ) = ð ›¼ 1 𠑦 ( 𠜂 ) . Here, ð ‘ âˆˆ ð ¶ [ 0 , 1 ] ∩ ð ¶ 1 ( 0 , 1 ] with ð ‘ ( ð ‘¡ ) > 0 on ( 0 , 1 ] and ð ‘ž ( ð ‘¡ ) is allowed to be discontinuous at ð ‘¡ = 0 . The fixed point theory in a cone is applied to achieve new and more general results for existence of multiple nonnegative solutions of the problem. The results are illustrated through examples.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:838947

DOI: 10.1155/2012/838947

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