Abstract
We consider the existence of minimal and maximal solutions of periodic boundary value problems for first-order impulsive integrodifferential equations of mixed-type on time scales by establishing a comparison result and using the monotone iterative technique.
Highlights
The theory of calculus on time scales was initiated by Stefan Hilger in his Ph.D. thesis in 1990 [3] in order to unify continuous and discrete analyses, and it has a tremendous potential for applications and has recently received much attention since his foundational work
For each interval J of R, we denote by JT = J ∩ T, f ∈ C[JT × R × R × R, R], J = [0, T], Ik ∈ C[R, R], where u(tk+) and u(tk−) represent right and left limits of u(t) at t = tk (k = 1, 2, . . . , p) in the sense of time scales, and in addition, if tk is right scattered, y(tk+) = y(tk), whereas if tk is left scattered, y(tk−) = y(tk), 2 Boundary Value Problems
The study of impulsive dynamic equations on time scales has been initiated by Henderson [4], Benchohra et al [5], and Atici and Biles [6]
Summary
The theory of calculus on time scales (see [1, 2] and references cited therein) was initiated by Stefan Hilger in his Ph.D. thesis in 1990 [3] in order to unify continuous and discrete analyses, and it has a tremendous potential for applications and has recently received much attention since his foundational work. For each interval J of R, we denote by JT = J ∩ T, f ∈ C[JT × R × R × R, R], J = [0, T], Ik ∈ C[R, R], where u(tk+) and u(tk−) represent right and left limits of u(t) at t = tk P) in the sense of time scales, and in addition, if tk is right scattered, y(tk+) = y(tk), whereas if tk is left scattered, y(tk−) = y(tk),
Sign-in/Register to view highlights & summary 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.
