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| We consider the existence of solutions for some nonresonance and resonance boundary value problems for the fractional p-Laplacian equation with the following form
$$
D_{0^+}^\beta\phi_p(D_{0^+}^\alpha x(t))=f(t,x(t),D_{0^+}^\alpha x(t)),
$$
where $\alpha,\beta\in (0,1],\ \phi_p(s)=|s|^{p-2}s, p>1$, and $D_{0^+}^\alpha$ is a Caputo fractional derivative. By using Schaefer's fixed point theorem and Ge-Mawhin's continuation theorem, some new existence results are obtained under the certain nonlinear growth conditions of the nonlinearity. |
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