Some problems of the spectral theory of a second-order differential equation with a variable unbounded operator coefficient

1974 ◽  
Vol 16 (5) ◽  
pp. 1079-1084
Author(s):  
V. M. Bruk
Keyword(s):  
Differential Equation ◽  
Spectral Theory ◽  
Unbounded Operator ◽  
Order Differential Equation ◽  
Second Order ◽  
Operator Coefficient ◽  
Second Order Differential Equation ◽  
Unbounded Operator Coefficient

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.

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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