Abstract
To prove the existence and uniqueness (or only the existence) of a bounded solution of a weakly nonlinear differential equation of the nth order, we use both the contraction mapping principle and the Tikhonov fixed-point theorem. We obtain an important qualitative estimate for the smallness of a nonlinear perturbation preserving the basic characteristics of the behavior of a linear equation (absolute stability or exponential dichotomy) under the passage to the nonlinear equation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
