On the C∞ -Goursat problem for some second order equations with variable coefficients

Discrete Galerkin Method for Higher Even-Order Integro-Differential Equations with Variable Coefficients

This paper presents discrete Galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. We use the generalized Jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. Numerical results are presented to demonstrate the effectiven...

Formulas for Solution of the Linear Differential Equations of the Second Order with the Variable Coefficients

Received: January 10, 2011 Accepted: February 10, 2011 doi:10.5539/jmr.v3n3p32 Abstract In this paper we obtained the formula for the common solution of the linear differential equation of the second order with the variable coefficients in the more common case. We also obtained the formula for the solution of the Cauchy problem.

Remarks on Invariant Method of the Second-Order Linear Differential Equations with Variable Coefficients

The Cauchy Problem for Complete Second-Order Hyperbol ic Differential Equations with Variable Domains of Operator Coefficients

Complete second-order hyperbolic differential equations with constant domains of operator coefficients were investigated in [1, 2]. In the case of variable domains of operator coefficients, second-order hyperbolic differential equations with a two-term leading part were analyzed in [3-5]. In the present paper, we investigate second-order hyperbolic differential equations with a three-term leadi...

On the Growth of Solutions of Some Second Order Linear Differential Equations With Entire Coefficients

In this paper, we investigate the order and the hyper-order of growth of solutions of the linear differential equation f ′′ +Q ( e ) f ′ + (A1e a1z +A2e 2) f = 0, where n > 2 is an integer, Aj (z) ( 6≡ 0) (j = 1, 2) are entire functions with max {σ (Aj) : j = 1, 2} < 1, Q (z) = qmz + · · · + q1z + q0 is a nonconstant polynomial and a1, a2 are complex numbers. Under some conditions, we prove tha...