scholarly journals An inverse problem for a second-order differential equation in a Banach space

2004 ◽  
Vol 2004 (12) ◽  
pp. 997-1005 ◽  
Author(s):  
Y. Eidelman
Keyword(s):  
Differential Equation ◽  
Unbounded Operator ◽  
Operator Function ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Cosine Operator Function ◽  
Second Order Differential Equation ◽  
The Right ◽  
Necessary And Sufficient

We consider the problem of determining the unknown term in the right-hand side of a second-order differential equation with unbounded operator generating a cosine operator function from the overspecified boundary data. We obtain necessary and sufficient conditions of the unique solvability of this problem in terms of location of the spectrum of the unbounded operator and properties of its resolvent.

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.

On the integrability of solutions of perturbed non-linear differential equations

1977 ◽  
Vol 77 (3-4) ◽  
pp. 309-318 ◽  
Author(s):  
Paul W. Spikes
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Differential Equations ◽  
Second Order Differential Equation ◽  
All Solutions ◽  
Non Linear ◽  
Linear Differential

SynopsisSufficient conditions are given to insure that all solutions of a perturbed non-linear second-order differential equation have certain integrability properties. In addition, some continuability and boundedness results are given for solutions of this equation.

Periodic Solutions for a Kind of Second Order Differential Equation with Multiple Delays

2011 ◽  
Vol 50-51 ◽  
pp. 27-31
Author(s):  
Mei Lan Tang ◽  
Xin Ge Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mawhin’S Continuation Theorem ◽  
Deviating Arguments ◽  
Second Order Differential Equation ◽  
Multiple Deviating Arguments

Based on Mawhin's continuation theorem and some analysis skill, some sufficient conditions for the existence of periodic solutions for a kind of second order differential equation with multiple deviating arguments are obtained. Results obtained in this paper extend the existing results.

scholarly journals Second-Order Differential Equation: Oscillation Theorems and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Shyam S. Santra ◽  
Omar Bazighifan ◽  
Hijaz Ahmad ◽  
Yu-Ming Chu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Delay ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Oscillation Theorems

Differential equations of second order appear in a wide variety of applications in physics, mathematics, and engineering. In this paper, necessary and sufficient conditions are established for oscillations of solutions to second-order half-linear delay differential equations of the form ς y u ′ y a ′ + p y u c ϑ y = 0 ,  for  y ≥ y 0 , under the assumption ∫ ∞ ς η − 1 / a = ∞ . Two cases are considered for a < c and a > c , where a and c are the quotients of two positive odd integers. Two examples are given to show the effectiveness and applicability of the result.

scholarly journals Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zaihong Wang ◽  
Jin Li ◽  
Tiantian Ma
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Duffing Equation ◽  
Deviating Argument ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions ◽  
The Given

We study the existence of periodic solutions of the second-order differential equationx′′+ax+-bx-+g(x(t-τ))=p(t), wherea,bare two constants satisfying1/a+1/b=2/n,n∈N,τis a constant satisfying0≤τ<2π,g,p:R→Rare continuous, andpis2π-periodic. When the limitslimx→±∞g(x)=g(±∞)exist and are finite, we give some sufficient conditions for the existence of2π-periodic solutions of the given equation.

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