Frequency methods in the theory of bounded solutions of nonlinear \(n\)th-order differential equations (existence, almost periodicity, and stability)
The author obtains new conditions for the existence of bounded solutions of higher-order non-linear differential equations. The classical contraction mapping principle and A. N. Tikhonov's fixed-point principle are used in the proofs of existence and uniqueness theorems. Stability results of a bounded solution are derived from results of M. A. Krasnosel'skii and A. V. Pokrovskii. Results in \(L_2\)- and \(L_\infty\)-theories are explicitly given.
bounded solutions of nonlinear differential equations
scientific article; zbMATH DE number 6105627