Boundedness in \(p\)-NFDEs (Q2765007)

The authors consider \(p\)-NFDEs of the form NEWLINE\[NEWLINE \frac{d}{dt}D(t, \overline{x}_t)=f(t, \overline{x}_t), NEWLINE\]NEWLINE where \(D, f: \Omega \rightarrow \mathbb{R}^n\) are given continuous functionals with \(D\) atomic at \(0\) on \(\Omega \), \(\Omega \) is an open subset of \(\mathbb{R}\times C([-1, 0], \mathbb{R}^n)\). By using Lyapunov functionals, they establish two boundedness criteria for \(p\)-NFDEs and improve some existing boundedness conditions for FDEs. To illustrate the advantages of the obtained results, two examples are also included.