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Wang, Yongqing; Liu, Lishan; Wu, Yonghong

Positive solutions for a fractional boundary value problem with changing sign nonlinearity. (English) Zbl 1247.35192

Abstr. Appl. Anal. 2012, Article ID 214042, 17 p. (2012).
Summary: We discuss the existence of positive solutions to the following fractional \(m\)-point boundary value problem with changing sign nonlinearity \(D^\alpha_{0+} u(t) + \lambda f(t, u(t)) = 0\), \(0 < t < 1\), \(u(0) = 0\), \(D^\beta_{0+} u(1) = \sum^{m-2}_{i=1} \eta_i D^\beta_{0+} u(\xi_i)\), where \(\lambda\) is a positive parameter, \(1 < \alpha \leq 2\), \(0 < \beta < \alpha - 1\), \(0 < \xi_1 < \cdots < \xi_{m-2} < 1\) with \(\sum^{m-2}_{i=1} \eta_i \xi^{\alpha -\beta -1}_i < 1\), \(D^\alpha_{0+}\) is the standard Riemann-Liouville derivative, \(f\) and may be singular at \(t = 0\) and/or \(t = 1\) and also may change sign. The work improves and generalizes some previous results.

Cited in 4 Documents

MSC:

35R11 Fractional partial differential equations
35B09 Positive solutions to PDEs
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References:

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