## Abstract and Applied Analysis

### Nontrivial Solutions for a Class of Fractional Differential Equations with Integral Boundary Conditions and a Parameter in a Banach Space with Lattice

#### Abstract

Existence of nontrivial solutions for the following fractional differential equation with integral boundary conditions ${D}_{0+}^{\alpha }u(t)+h(t)f(t,u(t))=0$, $0, $u(0)=u\text{'}(0)={u}^{\prime \prime }(0)=0$, $u(1)=\lambda {\int }_{0}^{\eta }u(s)\text{d}s$ is investigated by using results for the computation of topological degree under the lattice structure, where $3<\alpha \le 4$, $0<\eta \le 1$, $0\le \lambda {\eta }^{\alpha }/\alpha <1$, ${D}_{0+}^{\alpha }$ is the standard Riemann-Liouville derivative. $h(t)$ is allowed to be singular at $t=0$ and $t=1$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 391609, 18 pages.

Dates
First available in Project Euclid: 28 March 2013

https://projecteuclid.org/euclid.aaa/1364476007

Digital Object Identifier
doi:10.1155/2012/391609

Mathematical Reviews number (MathSciNet)
MR3004912

Zentralblatt MATH identifier
1257.35195

#### Citation

Zhang, Xingqiu; Wang, Lin. Nontrivial Solutions for a Class of Fractional Differential Equations with Integral Boundary Conditions and a Parameter in a Banach Space with Lattice. Abstr. Appl. Anal. 2012 (2012), Article ID 391609, 18 pages. doi:10.1155/2012/391609. https://projecteuclid.org/euclid.aaa/1364476007

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