Ulam–Hyers stability of elliptic partial differential equations in Sobolev spaces

Fixed Point Theory and the Ulam Stability

“…Let > 0 and , : → . We say that ( , ) is a -weakly Picard pair if there exists a weakly Picard operator ℎ : → such that More results on these as well as related problems can be found in [81][82][83][84][85][86][87][88][89][90][91][92][93][94][95].…”

Hyers–Ulam stability of delay differential equations of first order

“…, , , , –, many mathematicians paid attention to the problem of differential equations, for the papers concerning ordinary differential equations we refer the readers to , , , –, , , , . Further, the interested readers can see , , , , concerning the Hyers–Ulam stability of partial differential equations.…”

The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation

“…However, to the best knowledge of the authors, there exists no work in the literature which discusses the Hyers-Ulam stability of parabolic equations. Motivated by the above work [4,9], in this paper, we will consider the Hyers-Ulam stability for the following parabolic equation…”

“…András and Mészáros [4] considered the sufficient conditions of Hyers-Ulam stability for the following elliptic partial differential equation ∆u = f(x, u(x)) in Ω, u = 0 on ∂Ω.…”

“…Since then, there have been many papers dealing with the Hyers-Ulam stability for ordinary differential equations [1-3, 8, 13-15, 17-19] and partial differential equations [4,9]. Lungu and Popa [9] investigated the sufficient conditions of Hyers-Ulam stability for the following first order linear partial differential equation p(x, y) ∂u ∂x + q(x, y) ∂u ∂y = p(x, y)r(x)u + f(x, y).…”