Stability of the solution of a linear second-order differential equation with periodic coefficients

1974 ◽  
Vol 10 (4) ◽  
pp. 437-440
Author(s):  
V. I. Dvornikov ◽  
L. E. Shaikhet
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Periodic Coefficients ◽  
Second Order Differential Equation ◽  
Stability Of The Solution

scholarly journals Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Adil Misir ◽  
Banu Mermerkaya
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Order Differential Equation ◽  
Second Order ◽  
Periodic Coefficients ◽  
Second Order Differential Equation ◽  
Linear Differential ◽  
Critical Oscillation ◽  
Oscillation Constant

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.

THREE POSITIVE PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS WITH PERIODIC COEFFICIENTS

2005 ◽  
Vol 03 (02) ◽  
pp. 145-155 ◽  
Author(s):  
YUJI LIU ◽  
WEIGUO GE ◽  
ZHANJI GUI
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Positive Periodic Solutions ◽  
Periodic Coefficients ◽  
Second Order Differential Equation

We establish the existence of at least three positive periodic solutions to the second order differential equation with periodic coefficients [Formula: see text] where f is continuous with f(t + T, x) = f(t,x) for (t,x) ∊ R × R and T > 0, p, q are continuous and T-periodic with p > 0 and q ≥ 0. We accomplish this by making growth assumptions on f, which can apply to many more cases than those discussed in recent works. An example to illustrate the main result is given.

A mechanical method for the solution of second-order linear differential equations

1931 ◽  
Vol 27 (4) ◽  
pp. 546-552 ◽  
Author(s):  
E. C. Bullard ◽  
P. B. Moon
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Order Differential Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Mechanical Method ◽  
Order Linear ◽  
Second Order Differential Equation ◽  
Linear Differential

A mechanical method of integrating a second-order differential equation, with any boundary conditions, is described and its applications are discussed.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

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