A two parameter eigenvalue problem

1974 ◽  
Vol 10 (1) ◽  
pp. 39-50
Author(s):  
J.A. Rickard
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Order Differential Equation ◽  
Inviscid Fluid ◽  
Free Oscillations ◽  
Numerical Computations ◽  
Second Order Differential Equation ◽  
Independent Variable ◽  
Two Parameters ◽  
Two Parameter

An ordinary second order differential equation is considered in which the coefficients are dependent on two parameters ω and F as well as the independent variable μ. The equation arises in the study of free oscillations of incompressible inviscid fluid in global shells. An asymptotic technique is presented which estimates the eigenvaiues (that is the values of ω for which the solution is bounded for all |μ| ≤ 1) as functions of F, as F → ∞. The agreement of the results with numerical computations is also discussed.

scholarly journals Indefinite eigenvalue problem with eigenparameter in the two boundary conditions

1998 ◽  
Vol 21 (4) ◽  
pp. 775-784
Author(s):  
S. F. M. Ibrahim
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Boundary Conditions ◽  
Eigenfunction Expansion ◽  
Selfadjoint Operator ◽  
Order Differential Equation ◽  
Expansion Theorem ◽  
Compact Resolvent ◽  
Second Order Differential Equation ◽  
Eigenvalue Parameter

The object of this paper is to establish an expansion theorem for a regular indefinite eigenvalue problem of second order differential equation with an eigenvalue parameter,λin the two boundary conditions. We associated with this problem aJ-selfadjoint operator with compact resolvent defined in a suitable Krein space and then we develop an associated eigenfunction expansion theorem.

The Evaluation of Eigenvalues of a Differential Equation Arising in a Problem in Genetics

1962 ◽  
Vol 58 (4) ◽  
pp. 588-593 ◽  
Author(s):  
G. F. Miller ◽  
E. T. Goodwin
Keyword(s):  
Differential Equation ◽  
Asymptotic Behaviour ◽  
Order Differential Equation ◽  
Finite Size ◽  
Second Order ◽  
Random Drift ◽  
Smallest Eigenvalue ◽  
Second Order Differential Equation ◽  
Two Parameters

ABSTRACTThis paper concerns the determination of the smallest eigenvalue of a second order differential equation containing two parameters which arises in problems concerning genic selection under random drift in a population of finite size. A table of values is given, the method of computation is described, and the asymptotic behaviour for large values of one of the parameters is investigated.

Eigenvalue Problem for the Second Order Differential Equation with Nonlocal

2006 ◽  
Vol 11 (1) ◽  
pp. 13-32 ◽  
Author(s):  
B. Bandyrskii ◽  
I. Lazurchak ◽  
V. Makarov ◽  
M. Sapagovas
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Variable Coefficient ◽  
Order Differential Equation ◽  
Integral Condition ◽  
Second Order ◽  
Computational Results ◽  
Discrete Method ◽  
Complex Eigenvalues ◽  
Nonlocal Integral Condition

The paper deals with numerical methods for eigenvalue problem for the second order ordinary differential operator with variable coefficient subject to nonlocal integral condition. FD-method (functional-discrete method) is derived and analyzed for calculating of eigenvalues, particulary complex eigenvalues. The convergence of FD-method is proved. Finally numerical procedures are suggested and computational results are schown.

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.

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