Second order linear O.D.E. and Riccati equations

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

Second Order Linear and Nonlinear Differential Equations'

The General Solutions of Linear ODE and Riccati Equation

This paper gives out the general solutions of variable coefficients Linear ODE and Riccati equation by way of integral series E(X) and F (X). Such kinds of integral series are the generalized form of exponential function, and keep the properties of convergent and reversible.

The Riccati Sub-ODE Method For Fractional Differential-difference Equations

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

Linear Elliptic Equations of Second Order

The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...