Positive solutions for boundary-value problems of nonlinear fractional differential equations
In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem $$displaylines{ mathbf{D}_{0+}^alpha u(t)=f(t,u(t)),quad 0<t<1cr u(0)+u'(0)=0,quad u(1)+u'(1)=0 }$$ where $1<alphaleq...
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| Format: | Article |
| Language: | English |
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Texas State University
2006-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2006/36/abstr.html |
| Summary: | In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem $$displaylines{ mathbf{D}_{0+}^alpha u(t)=f(t,u(t)),quad 0<t<1cr u(0)+u'(0)=0,quad u(1)+u'(1)=0 }$$ where $1<alphaleq 2$ is a real number, and $mathbf{D}_{0+}^alpha$ is the Caputo's fractional derivative, and $f:[0,1]imes[0,+infty)o [0,+infty)$ is continuous. By means of a fixed-point theorem on cones, some existence and multiplicity results of positive solutions are obtained. |
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| ISSN: | 1072-6691 |