Multiple positive solutions for (n-1, 1)-type semipositone conjugate boundary value problems for coupled systems of nonlinear fractional differential equations
In this paper, we consider (n-1, 1)-type conjugate boundary value problem for coupled systems of the nonlinear fractional differential equation \begin{gather*}\left\{\begin{array}{ll} \mathbf{D}_{0+}^\alpha u+\lambda f(t,v)=0, 0<t<1, \lambda >0,\\ \mathbf{D}_{0+}^\alpha v+\lambda g(t,u)=...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2011-02-01
|
| 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=562 |
| Summary: | In this paper, we consider (n-1, 1)-type conjugate boundary value problem for coupled systems of the nonlinear fractional differential equation
\begin{gather*}\left\{\begin{array}{ll}
\mathbf{D}_{0+}^\alpha u+\lambda f(t,v)=0, 0<t<1, \lambda >0,\\
\mathbf{D}_{0+}^\alpha v+\lambda g(t,u)=0,\\
u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\
u(1)=v(1)=0,
\end{array}\right.\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 $f, g$ are continuous and semipositone. We give properties of Green's function of the boundary value problem, and derive an interval on $\lambda$ such that for any $\lambda$ lying in this interval, the semipositone boundary value problem has multiple positive solutions. |
|---|---|
| ISSN: | 1417-3875 1417-3875 |