Abstract
This paper deals with Ulam’s type stability for a class of Hill’s equations. In the two assertions of the main theorem, we obtain Ulam stability constants that are symmetrical to each other. By combining the obtained results, a necessary and sufficient condition for Ulam stability of a Hill’s equation is established. The results are generalized to nonhomogeneous Hill’s equations, and then application examples are presented. In particular, it is shown that if the approximate solution is unbounded, then there is an unbounded exact solution.
Highlights
IntroductionThe concept of Ulam’s type stability was posed by Ulam, and its development is remarkable
The concept of Ulam’s type stability was posed by Ulam, and its development is remarkable.Many researchers have studied this problem for functional equations
In 1998, Alsina and Ger [2] introduced this concept in the field of differential equations
Summary
The concept of Ulam’s type stability was posed by Ulam, and its development is remarkable. Many researchers have studied this problem for functional equations. See the book [1]. Written by Brzdek, Popa, Raşa, and Xu. In 1998, Alsina and Ger [2] introduced this concept in the field of differential equations. The study of Ulam’s type stability for differential equations continued to grow (see, [3,4,5,6,7,8,9,10]). Fukutaka and Onitsuka [11,12] dealt with Ulam’s type stability of the periodic linear differential equation y0 − p( x )y = 0
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