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Existence of solutions for a class of fractional boundary value problems via critical point theory. (English) Zbl 1235.34017

Summary: By the critical point theory, a new approach is provided to study the existence of solutions to the following fractional boundary value problem:

d dt1 2 0 D t -β (u ' (t))+1 2 t D T -β (u ' (t))+F(t,u(t))=0a.e.t[0,T],u(0)=u(T)=0,

where 0 D t -β and t D T -β are the left and right Riemann-Liouville fractional integrals of order 0β<1 respectively, F:[0,T]× N is a given function and F(t,x) is the gradient of F at x. The variational structure is established and various criteria on the existence of solutions are obtained.


MSC:
34A08Fractional differential equations
34B15Nonlinear boundary value problems for ODE
58E05Abstract critical point theory
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