Second-Order Linear Equations:
Sturm Picone Comparison Theorem of Second Order Linear Equations on Time Scales
... This paper studies Sturm-Picone comparison theorem of second-order linear equations on time scales. We first establish Picone identity on time scales and obtain our main result by using it. ...
12
Classification and criteria of the limit cases for singular second-order linear equations on time scales
... singular second-order linear equations on time ...the equations are divided into two cases: the limit-point and limit-circle cases just like the continuous and discrete ...of ...
17
Second Order Linear Differential Equations
... 12 Second Order Linear Differential Equations ...Homogeneous Equations A differential equation is a relation involving variables x y y y ...be linear if it is ...
11
Second Order Linear Differential Equations
... of equations, however, is very interesting in its own ...Euler equations can be easily solved in a way that is analogous to the characteristic equation method of solving constant coefficient homogeneous ...
45
SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS
... It’s not hard to think of some likely candidates for particular solutions of Equation 5 if we state the equation verbally. We are looking for a function such that a constant times its second derivative plus ...
9
On the stability of linear differential equations of second order
... In 1941, Hyers [7] obtained the result for p = 0. And then, Aoki [3] and Th. M. Rassias [24] generalized the above result of Hyers to the case where 0 6 p < 1. Moreover, Th. M. Rassias noticed in [24] that the proof ...
6
Fully non-linear parabolic differential equations of second order
... A thesis submitted for the degree of Doctor of Philosophy of the Australian National University.. for fully non 1 i near parabolic equations of second order in general for the no[r] ...
105
On decreasing solutions of second order nearly linear differential equations
... existing linear results; and second, as an analysis of the border case in the sense of the above described sub-linear and super-linear setting in (), where, in addition, a nonlinear- ity can ...
13
On homogeneous second order linear general quantum difference equations
... These equations are based on the general quantum difference operator D β , which is defined by D β f(t) = (f ( β (t)) – f (t))/( β (t) – t), β (t) = ...the second order linear homogeneous β ...
13
On the Growth of Solutions of Some Second Order Linear Differential Equations
... We investigate the growth of solutions of f Pzf Qzf 0, where P z and Qz are entire functions. When Pz e −z and Qz A 1 ze a 1 z A 2 ze a 2 z satisfy some conditions, we prove that every nonzero solution of the above ...
9
Oscillation of a class of second order linear impulsive differential equations
... differential equations are recognized as adequate mathematical models for studying evolution processes that are subject to abrupt changes in their states at certain ...differential equations have been the ...
12
On Approximate Solutions of Second Order Linear Partial Differential Equations
... Received August 15, 2012; revised September 15, 2012; accepted September 22, 2012 ABSTRACT In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential ...
7
Second Order Linear Partial Differential Equations. Part I
... For the equation to be of second order, a, b, and c cannot all be zero. Define its discriminant to be b 2 – 4ac. The properties and behavior of its solution are largely dependent of its type, as classified ...
23
ON THE ZERO DISTRIBUTION OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS IN THE
... of order ρ > 0 must have at least one Borel direction of order ρ (see ...In order to state our results, we note that in [13], [14], [15], the authors intro- duce the accumulation lines of ...
8
Oscillation of Second Order Quasi-linear Neutral Delay Differential Equations
... 1 School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, People’s Republic of China. 2 School of Mathematics and Systems Science, Shenyang Normal University, Shenyang, People’s Republic of ...
8
Some results of meromorphic solutions of second order linear differential equations
... Full list of author information is available at the end of the article Abstract In this paper, we investigate the growth and the zeros of difference of the first and second derivative of the solutions of the ...
14
Hyers ulam stability of exact second order linear differential equations
... exact second-order linear differential ...following equations: second-order linear differential equation with constant coefficients, Euler differential equation, Hermite’s ...
7
Power series method and approximate linear differential equations of second order
... However, it was inconvenient that he had to alter and apply the power series method with respect to each differential equation in order to study the Hyers-Ulam stability. Thus, it is inevitable to develop a power ...
9
Hyers Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order
... Recommended by Seppo Hassi The aim of this paper is to prove the stability in the sense of Hyers-Ulam of di ff erential equation of second order y pxy qxy rx 0. That is, if f is an approximate solution of ...
7
Properties of Meromorphic Solutions of a Class of Second Order Linear Differential Equations
... Abstract. This paper deals with the growth of meromorphic solutions of some second order linear differential equations, where it is assumed that the coefficients are meromorphic functions. Our ...
14