On the existence of solutions to periodic boundary value problems for fuzzy linear differential equations (Q385362)

In this paper, using generalized differentiability and switching points, the author establishes sufficient conditions for the existence of solution to the following fuzzy periodic boundary value problem: NEWLINE\[NEWLINEy'(t)=a(t)y(t)+b(t),t\in [0,T],\quad y(0)=y(T),NEWLINE\]NEWLINE where \(a:[0,T]\rightarrow\mathbb{R}\), \(b:[0,T] \rightarrow\mathbb{R}_{F}\), are continuous functions and where the coefficient a may have an arbitrary number of zeros on the interval \([0,T]\). A solution is built piecewise through a well-defined combination of solutions. The existence of solutions which are crisp at the switching points is also analyzed. Some illustrative examples are given.