Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0, 0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3, CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. Th...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/8196918 |
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| author | Wen Lian Zhanbing Bai |
| author_facet | Wen Lian Zhanbing Bai |
| author_sort | Wen Lian |
| collection | DOAJ |
| description | The existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0, 0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3, CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. The conclusion relies on the fixed-point index theory and the Leray-Schauder degree theory. The growth conditions of the nonlinearity with respect to the first eigenvalue of the related linear operator is given to guarantee the existence and multiplicity. |
| format | Article |
| id | doaj-art-5fe957bdeb9a4c9bbb54d67a4df57eb6 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-5fe957bdeb9a4c9bbb54d67a4df57eb62025-02-03T06:06:31ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/81969188196918Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value ProblemWen Lian0Zhanbing Bai1College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaThe existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary value problem (BVP) DC0+αyx+fx,yx=0, 0<x<1, y0=y′1=y″0=0 is established, where 2<α≤3, CD0+α is the Caputo fractional derivative, and f:0,1×0,∞⟶0,∞ is a continuous function. The conclusion relies on the fixed-point index theory and the Leray-Schauder degree theory. The growth conditions of the nonlinearity with respect to the first eigenvalue of the related linear operator is given to guarantee the existence and multiplicity.http://dx.doi.org/10.1155/2020/8196918 |
| spellingShingle | Wen Lian Zhanbing Bai Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem Journal of Function Spaces |
| title | Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem |
| title_full | Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem |
| title_fullStr | Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem |
| title_full_unstemmed | Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem |
| title_short | Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem |
| title_sort | eigenvalue criteria for existence of positive solutions to fractional boundary value problem |
| url | http://dx.doi.org/10.1155/2020/8196918 |
| work_keys_str_mv | AT wenlian eigenvaluecriteriaforexistenceofpositivesolutionstofractionalboundaryvalueproblem AT zhanbingbai eigenvaluecriteriaforexistenceofpositivesolutionstofractionalboundaryvalueproblem |