Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory

Jing Chen and X. H. Tang

Abstract and Applied Analysis, 2012, vol. 2012, 1-21

Abstract:

We study the existence and multiplicity of solutions for the following fractional boundary value problem: ( ð ‘‘ / ð ‘‘ ð ‘¡ ) ( ( 1 / 2 ) 0 ð · ð ‘¡ − ð ›½ ( ð ‘¢ ′ ( ð ‘¡ ) ) + ( 1 / 2 ) ð ‘¡ ð · ð ‘‡ − ð ›½ ( ð ‘¢ ′ ( ð ‘¡ ) ) ) + ∇ ð ¹ ( ð ‘¡ , ð ‘¢ ( ð ‘¡ ) ) = 0 , a . e . ð ‘¡ ∈ [ 0 , 𠑇 ] , ð ‘¢ ( 0 ) = ð ‘¢ ( 𠑇 ) = 0 , where ð ¹ ( ð ‘¡ , â‹… ) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:648635

DOI: 10.1155/2012/648635

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