Existence of Three Solutions for a Nonlinear Fractional Boundary Value Problem via a Critical Points Theorem

Chuanzhi Bai

Abstract and Applied Analysis, 2012, vol. 2012, 1-13

Abstract:

This paper is concerned with the existence of three solutions to a nonlinear fractional boundary value problem as follows: ( ð ‘‘ / ð ‘‘ ð ‘¡ ) ( ( 1 / 2 ) 0 ð · ð ‘¡ ð ›¼ − 1 ( ð ¶ 0 ð · ð ›¼ ð ‘¡ ð ‘¢ ( ð ‘¡ ) ) − ( 1 / 2 ) ð ‘¡ ð · ð ‘‡ ð ›¼ − 1 ( ð ¶ ð ‘¡ ð · ð ›¼ 𠑇 ð ‘¢ ( ð ‘¡ ) ) ) + 𠜆 ð ‘Ž ( ð ‘¡ ) ð ‘“ ( ð ‘¢ ( ð ‘¡ ) ) = 0 , a . e . ð ‘¡ ∈ [ 0 , 𠑇 ] , ð ‘¢ ( 0 ) = ð ‘¢ ( 𠑇 ) = 0 , where ð ›¼ ∈ ( 1 / 2 , 1 ] , and 𠜆 is a positive real parameter. The approach is based on a critical-points theorem established by G. Bonanno.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:963105

DOI: 10.1155/2012/963105

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