We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Let g ∈ L2(R) be a compactly supported function, whose integertranslates {Tkg}k∈Z form a partition of unity. We prove that for certain translationand modulation parameters, such a function g generates a Gabor frame, with a (non-canonical) dual generated by a finite linear combination h of the functions {Tkg}k∈Z; the coefficients in the linear combination are given explicitly. Thus, h has compac...

Môi tr??ng ??u t? là m?t trong nh?ng nhân t? có ?nh h??ng l?n t?i ho?t ??ng thu hút v?n tr?c ti?p n??c ngoài. Trong n?m qua, t?nh Thái Nguyên ?ã ??t ???c thành t?u nh?t ??nh vi?c c?i thi?n môi nh?m Tuy nhiên, làm th? nào ?? th? nâng cao h?n n?a ngoài bài toán mà c?n ph?i xem xét. Nghiên c?u c?a tác gi? phân tích thông qua ch? s? n?ng l?c c?nh tranh c?p t?nh, ??n vào Nguyên. Ngu?n li?u th? tích,...

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In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,ngeq 2$ and $g.c.d(s,...

‎In this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎As an application‎, ‎we give an example to demonstrate our main result.