Multiple Solutions for a Nonlinear Fractional Boundary Value Problem via Critical Point Theory
This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux, x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivativ...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2017-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2017/8548975 |
| Summary: | This paper is concerned with the existence of multiple solutions for the following nonlinear fractional boundary value problem: DT-αaxD0+αux=fx,ux, x∈0,T, u0=uT=0, where α∈1/2,1, ax∈L∞0,T with a0=ess infx∈0,Tax>0, DT-α and D0+α stand for the left and right Riemann-Liouville fractional derivatives of order α, respectively, and f:0,T×R→R is continuous. The existence of infinitely many nontrivial high or small energy solutions is obtained by using variant fountain theorems. |
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| ISSN: | 2314-8896 2314-8888 |