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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |