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Existence of solutions for multi point boundary value problems for fractional differential equations. (English) Zbl 1247.35190
Summary: By employing the Leggett-Williams fixed point theorem, we study the existence of three solutions in the multi point fractional boundary value problem $$\cases D^\alpha_{0^+}u(t)=f(t,u(t),u'(t)),\ t\in[0,1],\\ u(0)=u'(0)=0,\ u(1)-\sum^m_{i=1}a_iu(\xi_i)=\lambda,\endcases$$ where $2<\alpha\le 3$ and $m\ge 1$ are integers, $0<\xi_1<\xi_2< \cdots<\xi_n<1$ are constants, $\lambda\in(0,\infty)$ is a parameter, $\alpha_i>0$ for $1\le i\le m$ and $\sum^m_{i=1}a_i\xi_i\xi_i^{\alpha-1}<1$, $f\in C([0,1]\times[0,\infty)\times[0,\infty);[0,\infty))$.

35R11Fractional partial differential equations
35A01Existence problems for PDE: global existence, local existence, non-existence
Full Text: DOI
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