Peano Baker series convergence for matrix-valued functions of bounded variation.
In this paper we consider the random fuzzy differential equations and show their application by an example. Under suitable conditions the Peano type theorem on existence of solutions is proved. For our purposes, a notion of ε-solution is exploited.
Two theorems about period doubling bifurcations are proved. A special case, where one multiplier of the homogeneous solution is equal to +1 is discussed in the Appendix.
A convexity theorem for the period function T of Hamiltonian systems with separable variables is proved. We are interested in systems with non-monotone T. This result is applied to proving the uniqueness of critical orbits for second order ODE's.
The paper deals with the periodic boundary value problem (1) , , (2) , , where , , , , , and are continuous on , , , , {nonempty convex compact subsets of }, . The existence of such periodic solution is proven via Ky Fan’s fixed point theorem.