AN OSCILLATION THEOREM FOR A TWO-PARAMETER SYSTEM OF DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

1982 ◽  
Vol 5 (2) ◽  
pp. 107-118 ◽  
Author(s):  
M. Faiorman
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
System Of Differential Equations ◽  
Parameter System ◽  
Oscillation Theorem ◽  
Two Parameter

Stability regions for multi-parameter systems of periodic second order ordinary differential equations

1979 ◽  
Vol 84 (3-4) ◽  
pp. 249-257 ◽  
Author(s):  
Patrick J. Browne ◽  
B. D. Sleeman
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Parameter System ◽  
Stability Regions ◽  
The Stability ◽  
Image Position

SynopsisThis paper studies the stability regions associated with the multi-parameter systemwhere the functions qr(xr), ars(xr) are periodic and the system is subjected to periodic or semi-periodic boundary conditions.

A Note on Klein’s Oscillation Theorem for Periodic Boundary Conditions

1975 ◽  
Vol 17 (5) ◽  
pp. 749-755 ◽  
Author(s):  
M. Faierman
Keyword(s):  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Oscillation Theory ◽  
Continuous Functions ◽  
Oscillation Theorem ◽  
Image Position ◽  
Two Parameter

Recently Howe [4] has considered the oscillation theory for the two-parameter eigenvalue problem1a1bsubjected to the boundary conditions2a2bwhere for i = 1, 2, — ∞<ai<bi<∞, and qi are real-valued, continuous functions in [ai, bi], pi is positive in [ai, biz], and pi(ai)=pi(bi). Furthermore, it is also assumed that (A1B2—A2B1)≠0 for all values of x1 and x2 in their respective intervals.

Klein's Oscillation Theorem for Periodic Boundary Conditions

1971 ◽  
Vol 23 (4) ◽  
pp. 699-703 ◽  
Author(s):  
A. Howe
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Eigenvalue Problems ◽  
Periodic Boundary Conditions ◽  
Linear Differential Equations ◽  
Oscillation Theorem ◽  
Linear Differential ◽  
Image Position

Multiparameter eigenvalue problems for systems of linear differential equations with homogeneous boundary conditions have been considered by Ince [4] and Richardson [5, 6], and more recently Faierman [3] has considered their completeness and expansion theorems. A survey of eigenvalue problems with several parameters, in mathematics, is given by Atkinson [1].We consider the two differential equations:1a1bwhere p1’(x), q1(x), A1(x), B1(x) and p2’(y), q2(y), A2(y), B2(y) are continuous for x ∈ [a1, b1] and y ∈ [a2, b2] respectively, and p1 (x) > 0(x ∈ [a1, b1]), p2(y) > 0 (y ∈ [a2, b2]), p1(a1) = p1(b1), p2(a2) = p2(b2). The differential equations (1) will be subjected to the periodic boundary conditions.2a2bLet us consider a single differential equation

One-Dimensional Unsteady Periodic Flow Model with Boundary Conditions Constrained by Differential Equations

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Nhan T. Nguyen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Euler Equations ◽  
Periodic Boundary ◽  
Closed Loop ◽  
Fluid Transport ◽  
Periodic Boundary Conditions ◽  
Transport Systems ◽  
Variable Approach ◽  
Upwind Method

This paper describes a modeling method for closed-loop unsteady fluid transport systems based on 1D unsteady Euler equations with nonlinear forced periodic boundary conditions. A significant feature of this model is the incorporation of dynamic constraints on the variables that control the transport process at the system boundaries as they often exist in many transport systems. These constraints result in a coupling of the Euler equations with a system of ordinary differential equations that model the dynamics of auxiliary processes connected to the transport system. Another important feature of the transport model is the use of a quasilinear form instead of the flux-conserved form. This form lends itself to modeling with measurable conserved fluid transport variables and represents an intermediate model between the primitive variable approach and the conserved variable approach. A wave-splitting finite-difference upwind method is presented as a numerical solution of the model. An iterative procedure is implemented to solve the nonlinear forced periodic boundary conditions prior to the time-marching procedure for the upwind method. A shock fitting method to handle transonic flow for the quasilinear form of the Euler equations is presented. A closed-loop wind tunnel is used for demonstration of the accuracy of this modeling method.

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