Abstract
This paper is devoted to studying the Sobolev-type stochastic differential equations with Lévy noise and mixed fractional Brownian motion. Applying a method (principle) of comparability of functions by character of Shcherbakov recurrence, it characters at least one (or exactly one) solution with the same properties as the coefficients of the equation. We establish the existence of Poisson stable solutions for the Sobolev-type equation, which includes periodic solutions, quasi-periodic solutions, almost periodic solutions, almost automorphic solutions, etc. We also obtain the global asymptotical stability of bounded Poisson stable solutions and present an example to illustrate our theoretical results.
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.
