scholarly journals NEUMANN PROBLEM FOR AN ORDINARY SECOND - ORDER DIFFERENTIAL EQUATION WITH A DISTRIBUTED DIFFERENTIATION OPERATOR

2019 ◽  
Vol 5 (91) ◽  
pp. 30-37
Author(s):  
B.I. EFENDIEV ◽  
Keyword(s):  
Differential Equation ◽  
Neumann Problem ◽  
Order Differential Equation ◽  
Differentiation Operator ◽  
Second Order ◽  
Second Order Differential Equation

scholarly journals A global branch of solutions to a semilinear equation on an unbounded interval

1985 ◽  
Vol 101 (3-4) ◽  
pp. 273-282 ◽  
Author(s):  
C. A. Stuart
Keyword(s):  
Differential Equation ◽  
Neumann Problem ◽  
Order Differential Equation ◽  
Second Order ◽  
Semilinear Equation ◽  
Second Order Differential Equation ◽  
Unbounded Interval ◽  
The Neumann Problem ◽  
Global Branch

SynopsisFor a semilinear second order differential equation on (0, ∞), conditions are given for the bifurcation and asymptotic bifurcation in Lp of solutions to the Neumann problem. Bifurcation occurs at the lowest point of the spectrum of the linearised problem. Under stronger hypotheses, there is a global branch of solutions. These results imply similar conclusions for the same equation on R with appropriate symmetry.

scholarly journals Dirichlet problem for a second-order ordinary differential equation with a distributed differentiation operator

2021 ◽  
Vol 21 (4) ◽  
pp. 37-44
Author(s):  
B.I. Efendiev ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Dirichlet Problem ◽  
Function Method ◽  
Order Differential Equation ◽  
Variable Coefficients ◽  
Differentiation Operator ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Second Order Differential Equation

For an ordinary second-order differential equation with an operator of continuously distributed differentiation with variable coefficients, a solution to the Dirichlet problem is constructed using the Green’s function method.

Cauchy problem for second-order ordinary differential equation with continuously distributed differentiation operator

2020 ◽  
Vol 20 (1) ◽  
pp. 15-20
Author(s):  
B.I. Efendiev ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Order Differential Equation ◽  
Differentiation Operator ◽  
Second Order ◽  
Order Ordinary Differential Equation ◽  
Second Order Differential Equation ◽  
The Cauchy Problem

In this paper, we construct the fundamental solution for ordinary second-order differential equation with continuously distributed differentiation operator. With the help of fundamental solution the solution of the Cauchy problem is written out.

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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