Triple positive solutions for a boundary value problem of nonlinear fractional differential equation

• Main Author: Chuanzhi Bai
• Format: Article
• Language: English
• Published: University of Szeged 2008-07-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=338

In this paper, we investigate the existence of three positive solutions for the nonlinear fractional boundary value problem $D_{0+}^{\alpha} u(t) + a(t)f(t,u(t), u^{\prime \prime}(t))=0, \quad 0 < t < 1, \quad 3 < \alpha \leq 4,$ $u(0) = u^{\prime}(0) = u^{\prime \prime}(0)= u^{\prime \prime}(1)=0 $, where $D_{0+}^{\alpha}$ is the standard Riemann-Liouville fractional derivative. The method involves applications of a new fixed-point theorem due to Bai and Ge. The interesting point lies in the fact that the nonlinear term is allowed to depend on the second order derivative $u^{\prime \prime}$.