Laplace Transform and Semi-Hyers–Ulam–Rassias Stability of Some Delay Differential Equations

Abstract

In this paper, we study semi-Hyers–Ulam–Rassias stability and generalized semi-Hyers–Ulam–Rassias stability of differential equations x′t+xt−1=ft and x″t+x′t−1=ft,xt=0ift≤0, using the Laplace transform. Our results complete those obtained by S. M. Jung and J. Brzdek for the equation x′t+xt−1=0.

On an Approximate Solution of the Cauchy Problem for Systems of Equations of Elliptic Type of the First Order

“…[ 10 ]. Boundary problems, as well as numerical solutions of some problems, are considered in works [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ].…”

Regularized Solution of the Cauchy Problem in an Unbounded Domain

“…In [12], the Cauchy problem for the Helmholtz equation in an arbitrary bounded plane domain was considered. Certain boundary value problems and the determination of numerical solutions was investigated in [13][14][15][16][17][18][19][20][21][22][23][24][25]. In [21] is studied the Cauchy problem of a modified Helmholtz equation.…”

Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations

“…The field then continued to grow rapidly. We mention the works [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A summary of certain works can be consulted in [20,21].…”