Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems of nonlinear fractional differential equations
In this paper, we consider (n-1, 1)-type conjugate boundary value problem for the nonlinear fractional differential equation \begin{gather*}\begin{array}{ll} \mathbf{D}_{0+}^\alpha u(t)+\lambda f(t,u(t))=0,\quad 0<t<1, \lambda >0,\\ u^{(j)}(0)=0, 0\leq j\leq n-2,\\ u(1)=0, \end{arra...
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| Format: | Article |
| Language: | English |
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University of Szeged
2010-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=496 |
| Summary: | In this paper, we consider (n-1, 1)-type conjugate boundary value problem for the nonlinear fractional differential equation
\begin{gather*}\begin{array}{ll}
\mathbf{D}_{0+}^\alpha u(t)+\lambda f(t,u(t))=0,\quad 0<t<1, \lambda >0,\\
u^{(j)}(0)=0, 0\leq j\leq n-2,\\
u(1)=0,
\end{array}\end{gather*}
where $\lambda$ is a parameter, $\alpha\in(n-1, n]$ is a real number and $n\geq 3$, and $\mathbf{D}_{0+}^\alpha$ is the Riemann-Liouville's fractional derivative, and $f$ is continuous and semipositone. We give properties of Green's function of the boundary value problems, and derive an interval of $\lambda$ such that any $\lambda$ lying in this interval, the semipositone boundary value problem has multiple positive solutions. |
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| ISSN: | 1417-3875 |