[HTML][HTML] Laplace transform and Hyers–Ulam stability of linear differential equations
H Rezaei, SM Jung, TM Rassias - Journal of Mathematical Analysis and …, 2013 - Elsevier
H Rezaei, SM Jung, TM Rassias
Journal of Mathematical Analysis and Applications, 2013•ElsevierIn this paper, we prove the Hyers–Ulam stability of a linear differential equation of the nth
order. More precisely, applying the Laplace transform method, we prove that the differential
equation y (n)(t)+∑ k= 0n− 1αky (k)(t)= f (t) has Hyers–Ulam stability, where αk is a scalar, y
and f are n times continuously differentiable and of exponential order, respectively.
order. More precisely, applying the Laplace transform method, we prove that the differential
equation y (n)(t)+∑ k= 0n− 1αky (k)(t)= f (t) has Hyers–Ulam stability, where αk is a scalar, y
and f are n times continuously differentiable and of exponential order, respectively.
In this paper, we prove the Hyers–Ulam stability of a linear differential equation of the nth order. More precisely, applying the Laplace transform method, we prove that the differential equation y(n)(t)+∑k=0n−1αky(k)(t)=f(t) has Hyers–Ulam stability, where αk is a scalar, y and f are n times continuously differentiable and of exponential order, respectively.
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