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Existence and multiplicity of solutions for some fractional boundary value problem via critical point theory. (English) Zbl 1235.34011
Summary: We study the existence and multiplicity of solutions for the following fractional boundary value problem: $(d/dt)((1/2)_0 D^{-\beta}_t (u'(t)) + (1/2)_t D^{-\beta}_T (u'(t))) + \nabla F(t, u(t)) = 0$, a. e. $t \in [0, T], u(0) = u(T) = 0$, where $F(t, \cdot)$ are superquadratic, asymptotically quadratic, and subquadratic, respectively. Several examples are presented to illustrate our results.

##### MSC:
 34A08 Fractional differential equations 34B99 Boundary value problems for ODE
##### Keywords:
fractional boundary value problem
Full Text:
##### References:
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