Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions

作者：Jia, Mei^*; Liu, Xiping

来源：Applied Mathematics and Computation, 2014, 232: 313-323.

DOI：10.1016/j.amc.2014.01.073

• Fractional differential equations
• Integral boundary value problems
• Multiplicity of solutions
• Upper and lower solutions
• Leray-Schauder degree theory

In this paper, we study the existence of multiple solutions for the integral boundary value problems of fractional differential equations by the method of upper and lower solutions and Leray-Schauder degree theory. The sufficient conditions about the existence of at least three solutions are obtained. Moreover, it is proved that the integral boundary value problem has at least three positive solutions under the conditions of M = 0 and f is nonnegative. By given two upper and lower solutions which can be easily obtained through our methods, we can present the existence theorem of at least three solutions. Two examples are also included to illustrate the effectiveness of the proposed results.

• 出版日期2014-4-1
• 单位上海理工大学