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In this paper, we present some theorems on impulsive periodic boundary value problems with fractional derivative dependence. In particular, we discuss the existence of solutions of a class of fractional-order impulsive periodic boundary values with nonlinear terms and impulsive terms satisfying certain growth conditions. Three examples are provided to illustrate our results.

In this paper, we study the existence of nontrivial solutions for the 2nth Lidstone boundary value problem with a sign-changing nonlinearity. Under some conditions involving the eigenvalues of a linear operator, we use the topological degree theory to obtain our main results.