Solution Matching for a Second Order Boundary Value Problem on Time Scales

Aprillya Lanz and Ana Tameru

International Journal of Mathematics and Mathematical Sciences, 2012, vol. 2012, 1-7

Abstract:

Let ð •‹ be a time scale such that ð ‘Ž < ð ‘ ; ð ‘Ž , ð ‘ âˆˆ ð •‹ . We will show the existence and uniqueness of solutions for the second-order boundary value problem 𠑦 Δ Δ ( ð ‘¡ ) = ð ‘“ ( ð ‘¡ , 𠑦 ( ð ‘¡ ) , 𠑦 Δ ( ð ‘¡ ) ) , ð ‘¡ ∈ [ ð ‘Ž , ð ‘ ] ð •‹ , 𠑦 ( ð ‘Ž ) = ð ´ , 𠑦 ( ð ‘ ) = ð µ , by matching a solution of the first equation satisfying boundary conditions on [ ð ‘Ž , ð ‘ ] ð •‹ with a solution of the first equation satisfying boundary conditions on [ ð ‘ , ð ‘ ] ð •‹ , where ð ‘ âˆˆ ( ð ‘Ž , ð ‘ ) ð •‹ .

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:465867

DOI: 10.1155/2012/465867

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