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.

we focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of it¨o type, in particular, parabolic equations. the main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.

Abstract The paper investigates stability properties of solutions optimal control problems constrained by semilinear parabolic partial differential equations. Hölder or Lipschitz dependence the solution on perturbations are obtained for in which equation and objective functional affine with respect to control. may appear both nonlinearly depend state variables. main results based an extension r...

the use of accelerated temperature stability studies using the arrhenius relationship is routine for estimating the stability of a drug at room temperature. therefore, the acceleration method is used to determine the expiration date of dexamethasone aqueous formulation manufactured in iran. a high-performance liquid chromatography (hplc) method utilizing ultraviolet (uv) detection for dexametha...