Geodesic
Unified Massera type theorems for dynamic equations on time scales
Filomat, Tome 37 (2023) no. 8, p. 2405

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DOI

In this paper, we aim to obtain Massera type theorems for both linear and nonlinear dynamic equations by using a generalized periodicity notion, namely (T, λ)-periodicity, on time scales. To achieve this task, first we define a new boundedness concept so-called λ-boundedness, and then we establish a linkage between the existence of λ-bounded solutions and (T, λ)-periodic solutions of dynamic equations in both linear and nonlinear cases. In our analysis, we assume that the time scale T is periodic in shifts δ ± which does not need to be translation invariant. Thus, outcomes of this work are valid for a large class of time-domains not restricted to T = R or T = Z.
DOI : 10.2298/FIL2308405K
Classification : 34N05, 34C25 34K13
Keywords: Time scale, shift operator, (T, λ)-periodic, (T, λ)-symmetric, Massera’s theorem 
Halis Can Koyuncuoğlu. Unified Massera type theorems for dynamic equations on time scales. Filomat, Tome 37 (2023) no. 8, p. 2405 . doi: 10.2298/FIL2308405K
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     author = {Halis Can Koyuncuo\u{g}lu},
     title = {Unified {Massera} type theorems for dynamic equations on time scales},
     journal = {Filomat},
     pages = {2405 },
     year = {2023},
     volume = {37},
     number = {8},
     doi = {10.2298/FIL2308405K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2308405K/}
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