HYERS–ULAM–RASSIAS STABILITY FOR NONAUTONOMOUS DYNAMICS
Copyright policy )HYERS–ULAM–RASSIAS STABILITY FOR NONAUTONOMOUS DYNAMICS
The authors study semilinear equations \begin{align*} x'&=A(t)x+f(t,x),\\ x_{n+1}&=A_nx_n+f_n(x_n) \end{align*} on the nonnegative half-line in a Banach space \(X\). Provided the linear part is uniformly exponentially stable, Hyers-Ulam-Rassias stability is established, if the (uniform) Lipschitz constant of the nonlinearity is small. The proof is based on the contraction mapping principle.
exponential stability, nonautonomous dynamics, Perturbations of ordinary differential equations, Nonautonomous smooth dynamical systems, Hyers-Ulam-Rassias stability, Hybrid systems of ordinary differential equations, Additive difference equations
exponential stability, nonautonomous dynamics, Perturbations of ordinary differential equations, Nonautonomous smooth dynamical systems, Hyers-Ulam-Rassias stability, Hybrid systems of ordinary differential equations, Additive difference equations
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