Monotonic Positive Solutions of Nonlocal Boundary Value Problems for a Second-Order Functional Differential Equation

A. M. A. El-Sayed, E. M. Hamdallah and Kh. W. El-kadeky

Abstract and Applied Analysis, 2012, vol. 2012, 1-12

Abstract:

We study the existence of at least one monotonic positive solution for the nonlocal boundary value problem of the second-order functional differential equation ð ‘¥ î…ž î…ž ( ð ‘¡ ) = ð ‘“ ( ð ‘¡ , ð ‘¥ ( 𠜙 ( ð ‘¡ ) ) ) , ð ‘¡ ∈ ( 0 , 1 ) , with the nonlocal condition ∑ ð ‘š 𠑘 = 1 ð ‘Ž 𠑘 ð ‘¥ ( ð œ ð ‘˜ ) = ð ‘¥ 0 , ð ‘¥ î…ž ∑ ( 0 ) + ð ‘› ð ‘— = 1 ð ‘ ð ‘— ð ‘¥ î…ž ( 𠜂 ð ‘— ) = ð ‘¥ 1 , where ð œ ð ‘˜ ∈ ( ð ‘Ž , ð ‘‘ ) ⊂ ( 0 , 1 ) , 𠜂 ð ‘— ∈ ( ð ‘ , ð ‘’ ) ⊂ ( 0 , 1 ) , and ð ‘¥ 0 , ð ‘¥ 1 > 0 . As an application the integral and the nonlocal conditions ∫ ð ‘‘ ð ‘Ž ð ‘¥ ( ð ‘¡ ) ð ‘‘ ð ‘¡ = ð ‘¥ 0 , ð ‘¥ î…ž ( 0 ) + ð ‘¥ ( ð ‘’ ) − ð ‘¥ ( ð ‘ ) = ð ‘¥ 1 will be considered.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:489353

DOI: 10.1155/2012/489353

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