Solutions for impulsive fractional differential equations via variational methods (Q288773)

Summary: We investigate boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of \textit{J. Mawhin} and \textit{M. Willem} [Critical point theory and Hamiltonian systems. New York etc.: Springer-Verlag. (1989; Zbl 0676.58017)]. Then by the variational methods and a very recent critical points theorem of \textit{G. Bonanno} and \textit{S. A. Marano} [Appl. Anal. 89, No. 1, 1-10 (2010; Zbl 1194.58008)], the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results.