Hyers–Ulam stability of the linear differential operator with nonconstant coefficients

2012 ◽  
Vol 219 (4) ◽  
pp. 1562-1568 ◽  
Author(s):  
Dorian Popa ◽  
Ioan Raşa
Keyword(s):  
Differential Operator ◽  
Linear Differential Operator ◽  
Ulam Stability ◽  
Linear Differential

scholarly journals Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1451
Author(s):  
Liviu Cădariu ◽  
Dorian Popa ◽  
Ioan Raşa
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Operator ◽  
Global Solution ◽  
Linear Differential Operator ◽  
Second Order ◽  
Order Differential Operator ◽  
Ulam Stability ◽  
Riccati Differential Equation ◽  
Linear Differential

In this paper, we obtain a result on Ulam stability for a second order differential operator acting on a Banach space. The result is connected to the existence of a global solution for a Riccati differential equation and some appropriate conditions on the coefficients of the operator.

Method of Forced Monotonicity for Conjugate type Boundary Value Problems for Ordinary Differential Equations

1988 ◽  
Vol 31 (1) ◽  
pp. 79-84
Author(s):  
P. W. Eloe ◽  
P. L. Saintignon
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Ordinary Differential Equations ◽  
Linear Differential Operator ◽  
Boundary Value ◽  
Linear Differential ◽  
Type Boundary ◽  
Sign Conditions ◽  
Conjugate Type

AbstractLet I = [a, b] ⊆ R and let L be an nth order linear differential operator defined on Cn(I). Let 2 ≦ k ≦ n and let a ≦ x1 < x2 < … < xn = b. A method of forced mono tonicity is used to construct monotone sequences that converge to solutions of the conjugate type boundary value problem (BVP) Ly = f(x, y),y(i-1) = rij where 1 ≦i ≦ mj, 1 ≦ j ≦ k, mj = n, and f : I X R → R is continuous. A comparison theorem is employed and the method requires that the Green's function of an associated BVP satisfies certain sign conditions.

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