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Zbl 1235.34027
Wang, Yongqing; Liu, Lishan; Wu, Yonghong
Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 17, 6434-6441 (2011). ISSN 0362-546X

Summary: We discuss the existence of positive solutions to the following fractional boundary value problem with changing sign nonlinearity. $$\cases D^\alpha_{0+}u(t)+\lambda f(t,u(t))=0,\ 0<t<1,\\ u(0)=u'(0)=u(1)=0.\endcases$$ where $2<\alpha\le 3$ is a real number, $D^\alpha_{0+}$ is the standard Riemann-Liouville derivative, $\lambda$ is a positive parameter, $f$ may change sign and may be singular at $t=0,1$.
MSC 2000:
*34A08
34B18 Positive solutions of nonlinear boundary value problems
34B16 Singular nonlinear boundary value problems

Keywords: fractional differential equation; positive solution; Green function; semipositone; boundary value problem

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