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Existence results for fractional boundary value problem via critical point theory. (English) Zbl 1258.34015

Summary: By the critical point theory, a boundary value problem is discussed for a fractional differential equation containing the left and right fractional derivative operators, and various criteria on the existence of solutions are obtained. To the authors’ knowledge, this is the first time, the existence of solutions to the fractional boundary value problem is dealt with by using critical point theory.

MSC:

34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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