Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory
We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/648635 |
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| author | Jing Chen X. H. Tang |
| author_facet | Jing Chen X. H. Tang |
| author_sort | Jing Chen |
| collection | DOAJ |
| description | We study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results. |
| format | Article |
| id | doaj-art-5acc26c0934d4cfe9ea3903e416e3ea0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5acc26c0934d4cfe9ea3903e416e3ea02025-02-03T06:01:05ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/648635648635Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point TheoryJing Chen0X. H. Tang1School of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematical Sciences and Computing Technology, Central South University, Changsha, Hunan 410083, ChinaWe study the existence and multiplicity of solutions for the following fractional boundary value problem: (𝑑/𝑑𝑡)((1/2)0𝐷𝑡−𝛽(𝑢′(𝑡))+(1/2)𝑡𝐷𝑇−𝛽(𝑢′(𝑡)))+∇𝐹(𝑡,𝑢(𝑡))=0,a.e.𝑡∈[0,𝑇],𝑢(0)=𝑢(𝑇)=0, where 𝐹(𝑡,⋅) are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results.http://dx.doi.org/10.1155/2012/648635 |
| spellingShingle | Jing Chen X. H. Tang Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory Abstract and Applied Analysis |
| title | Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory |
| title_full | Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory |
| title_fullStr | Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory |
| title_full_unstemmed | Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory |
| title_short | Existence and Multiplicity of Solutions for Some Fractional Boundary Value Problem via Critical Point Theory |
| title_sort | existence and multiplicity of solutions for some fractional boundary value problem via critical point theory |
| url | http://dx.doi.org/10.1155/2012/648635 |
| work_keys_str_mv | AT jingchen existenceandmultiplicityofsolutionsforsomefractionalboundaryvalueproblemviacriticalpointtheory AT xhtang existenceandmultiplicityofsolutionsforsomefractionalboundaryvalueproblemviacriticalpointtheory |