Topics in singular perturbations

Theory of Ordinary Differential Equations

1956 • 6,499 citations

Theory of ordinary differential equations

1956 • 5,705 citations

Lectures on Cauchy's Problem in Linear Partial Differential Equations

1953 • 2,155 citations

Asymptotic expansions for ordinary differential equations

1965 • 1,677 citations

Modern Developments in Fluid Dynamics

1939 • 1,629 citations

Perturbation Methods in Applied Mathematics

1969 • 1,049 citations

Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder

1957 • 871 citations

Principles and Techniques of Applied Mathematics

1957 • 866 citations

Nonlinear Vibrations in Mechanical and Electrical Systems

1950 • 831 citations

Stability by Liapunov's Direct Method With Applications

1962 • 716 citations

Ordinary Differential Equations

1966 • 544 citations

Non‐coercive boundary value problems

1965 • 431 citations

PERTURBATION METHODS IN APPLIED MATHEMATICS

1969 • 381 citations

Perturbation Techniques in Mathematics, Physics, and Engineering.

1965 • 332 citations

On the mathematical status of the pseudo-steady state hypothesis of biochemical kinetics

1967 • 286 citations

On the asymptotic character of the solutions of certain linear differential equations containing a parameter

1908 • 279 citations

Singular perturbations on the infinite interval

1966 • 275 citations

Störungstheorie der Spektralzerlegung

1937 • 263 citations

ASYMPTOTIC BEHAVIOUR OF SOLUTIONS TO CERTAIN PROBLEMS INVOLVING NON-LINEAR DIFFERENTIAL EQUATIONS CONTAINING A SMALL PARAMETER MULTIPLYING THE HIGHEST DERIVATIVES

1963 • 247 citations

Ordinary Differential Equations

1991 • 242 citations

Asymptotic Expansions of Navier-Stokes Solutions for Small Reynolds Numbers

1957 • 177 citations

Low Reynolds Number Flow Past a Circular Cylinder

1957 • 167 citations

Asymptotic phenomena in mathematical physics

1955 • 163 citations

Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type

1966 • 154 citations

Fluid Mechanics and Singular Perturbations

1967 • 151 citations

The role of coordinate systems in boundary-layer theory

1954 • 146 citations

Stability by Liapunov's direct method with applications

1962 • 104 citations

Some remarks on the flat plate boundary layer

1949 • 102 citations

Störungstheorie der Spektralzerlegung. IV

1940 • 99 citations

The First Boundary Value Problem for εΔu + A(x, y)u x + B(x, y)u y + C(x, y)u = D(x, y) for Small ε

1950 • 98 citations

Periodic Solutions of Singularly Perturbed Systems

1955 • 93 citations

Störungstheorie der Spektralzerlegung

1939 • 89 citations

Sur certaines équations paraboliques non linéaires

1965 • 88 citations

Singular perturbations of non-linear oscillations

1946 • 85 citations

Quantum mechanics and asymptotic series

1933 • 85 citations

The two variable expansion procedure for the approximate solution of certain nonlinear differential equations

1962 • 78 citations

Perturbations of discontinuous solutions of non-linear systems of differential equations

1950 • 73 citations

International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics

1963 • 69 citations

Störungstheorie der Spektralzerlegung

1937 • 69 citations

A boundary value problem for a nonlinear differential equation with a small parameter

1952 • 69 citations

St�rungstheorie der Spektralzerlegung. V

1941 • 68 citations

IV. FORCED OSCILLATIONS IN NONLINEAR SYSTEMS

1950 • 66 citations

Second-order linear parabolic equations with a small parameter

1968 • 64 citations

Singular perturbations of boundary value problems for nonlinear differential equations of the second order

1956 • 62 citations

Boundary Layer Problems in Applied Mechanics

1953 • 60 citations

ASYMPTOTIC EXPANSIONS

1964 • 48 citations

The solutions of second order linear ordinary differential equations about a turning point of order two

1955 • 47 citations

On the Asymptotic Solution of Boundary Value Problems for Ordinary Differential Equations Containing a Parameter

1944 • 46 citations

Rate of convergence in singular perturbations

1968 • 45 citations

Asymptotic solutions of a system of linear ordinary differential equations containing a parameter.

1962 • 43 citations

Reduction of the order of a linear ordinary differential equation containing a small parameter

1963 • 41 citations

Stability in systems with parameter

1967 • 40 citations

VI. Asymptotic Expansions of Solutions of Systems of Ordinary Linear Differential Equations Containing a Parameter

1953 • 39 citations

Sur reduction analytique d'un systeme d'equations differentielles ordinaires lineaires contenant un parametre

1958 • 38 citations

Asymptotic developments I. Fundamental theorems of asymptotics

1954 • 38 citations

Singular perturbations of boundary value problems for linear ordinary differential equations involving two parameters

1967 • 38 citations

Considerations regarding the mathematical basis for Prandtl's boundary layer theory

1968 • 37 citations

Phénomènes de perturbation singulière dans les problèmes aux limites

1960 • 37 citations

A boundary value problem for a singularly perturbed differential equation

1955 • 36 citations

Asymptotic Solutions of Certain Ordinary Differential Equations Associated with Multiple Roots of the Characteristic Equation

1936 • 35 citations

On systems of ordinary differential equations with several parameters multiplying the derivatives

1969 • 35 citations

Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, II boundary value problems

1968 • 35 citations

Asymptotic theory of second order differential equations with two simple turning points

1958 • 35 citations

Singular perturbations for partial differential equations

1968 • 34 citations

Exemples concrets d'étude asymptotique d'oscillations de relaxation

1944 • 34 citations

Asymptotic solutions of differential equations and their applications

1965 • 34 citations

Singular perturbation of eigenvalue problems for linear differential equations of even order

1955 • 33 citations

Vibrations of rotating beams with tip mass

1961 • 33 citations

Sur les équations hyperboliques avec petit paramètre

1963 • 33 citations

On Certain Relaxation Oscillations: Asymptotic Solutions

1965 • 29 citations

Étude asymptotique des oscillations de relaxation

1943 • 29 citations

I. Van der Pol’s Equation for Relaxation Oscillations

1953 • 29 citations

Studies in Nonlinear Vibration Theory

1951 • 29 citations

Periodic Solutions of van der Pol's Equations with Large Damping Coefficientlambda = 0 sim 10

1960 • 28 citations

Bounded and almost periodic solutions of singularly perturbed equations

1961 • 28 citations

Singular Perturbations of Boundary Value Problems Involving Ordinary Differential Equations

1963 • 28 citations

Nonlinear boundary-value problems arising in chemical reactor theory

1968 • 27 citations

On the behavior of the solution of the telegraphist’s equation for large velocities

1967 • 27 citations

On the asymptotic solutions of a class of ordinary differential equations of the fourth order. I. Existence of regular formal solutions

1960 • 27 citations

On a nonlinear boundary value problem involving a small parameter

1962 • 27 citations

Asymptotic solution of boundary value problems for the differential equation ΔU+λ∂∂xU=λf(x,y)

1944 • 26 citations

Numerical Study of Periodic Solutions of the van der Pol Equation

1963 • 25 citations

Approximate solutions of a nonlinear boundary value problem

1968 • 25 citations

ON THE LIMIT OF SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS AS THE RETARDATION APPROACHES ZERO

1959 • 25 citations

Boundary layer problems in applied mathematics

1954 • 24 citations

Singular perturbations of two-point boundary problems for systems of ordinary differential equations

1960 • 24 citations

On a Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter

1969 • 23 citations

Almost periodic solutions of singularly perturbed systems of differential equations

1968 • 23 citations

Non‐linear deflection of thin elastic plates under tension

1961 • 22 citations

A boundary value problem for certain nonlinear second order differential equations with a small parameter

1968 • 22 citations

On a class of singular perturbation problems

1964 • 22 citations

Two-Variable Expansions for Singular Perturbations

1968 • 22 citations

The condition of regular degeneration for singularly perturbed systems of linear differential-difference equations

1966 • 20 citations

Étude asymptotique des oscillations de relaxation (suite et fin)

1943 • 19 citations

The condition of regular degeneration for singularly perturbed linear differential-difference equations

1965 • 19 citations

On the Approximation of Double Limits by Single Limits and the Kaplun Extension Theorem

1967 • 18 citations

Singular perturbations of a boundary value problem for a nonlinear system of differential equations

1962 • 18 citations

Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, I eigenvalue problems

1968 • 18 citations

On a nonlinear boundary value problem with a small parameter multiplying the highest derivative

1966 • 16 citations

Note on the Preceding Two Papers

1957 • 16 citations

Singular perturbations of Cauchy's problem

1965 • 15 citations

SINGULAR PERTURBATIONS AND SOME NON LINEAR BOUNDARY VALUE PROBLEMS

1963 • 15 citations

A boundary value problem for a singularly perturbed differential equation

1958 • 15 citations

Continuity properties on the retardation in the theory of difference-differential equations

1961 • 14 citations

Asymptotic Methods for Systems of Differential Equations in which some Variables have very Short Response Times

1968 • 14 citations

Error bounds for asymptotic solutions of differential equations.I. Distinct eigenvalue case

1966 • 13 citations

Singular perturbations of a boundary value problem for a system of nonlinear ordinary differential equations

1967 • 13 citations

Differential Equations with a Small Parameter Attached to the Highest Derivatives and Some Problems in the Theory of Oscillations

1960 • 13 citations

THE WORK OF TIKHONOV AND HIS PUPILS ON ORDINARY DIFFERENTIAL EQUATIONS CONTAINING A SMALL PARAMETER

1967 • 13 citations

Perturbations of Discontinuous Solutions of Non-Linear Systems of Differential Equations

1947 • 12 citations

The parabolic equation as a limiting case of a certain elliptic equation

1962 • 12 citations

A singular perturbation method. Part II

1968 • 11 citations

Singular perturbations of eigenvalue problems

1961 • 11 citations

A Method of Error Estimation in Singular Perturbation Problems with Application to the Restricted Three Body Problem

1967 • 11 citations

On the uniqueness of solutions of linear differential equations

1968 • 11 citations

The Importance of Asymptotic Analysis in Applied Mathematics

1966 • 10 citations

On singular perturbation in non well posed problems

1967 • 10 citations

On the asymptotic solution of nonhomogeneous ordinary differential equations with a large parameter

1965 • 10 citations

VII. ON THE CONSTRUCTION OF PERIODIC SOLUTIONS OF SINGULAR PERTURBATION PROBLEMS

1950 • 10 citations

A singular perturbation method. Part I

1968 • 10 citations

On a singular perturbation problem concerning hyperbolic equations

1964 • 9 citations

Degeneration of the solutions of certain well-posed systems of partial differential equations depending on a small parameter

1966 • 9 citations

Perturbation solutions and asymptotic solutions in boundary layer theory

1967 • 9 citations

On the asymptotic solution of boundary value problems for nonhomogeneous ordinary differential equations containing a parameter

1969 • 9 citations

Periodic Solutions of Singular Perturbation Problems

1963 • 8 citations

Asymptotic decomposition of systems of linear differential equations having poles with respect to a parameter

1964 • 8 citations

First Order Partial Differential Equations Containing a Small Parameter

1955 • 7 citations

Singular Perturbation Eigenvalues by a Method of Undetermined Coefficients

1963 • 7 citations

Asymptotic Solutions of the First Boundary Value Problem for a Fourth-Order Elliptic Partial Differential Equation

1956 • 6 citations

The Importance of Asymptotic Analysis in Applied Mathematics

1966 • 6 citations

Singular perturbation problems of systems of two ordinary analytic differential equations

1963 • 6 citations

The first boundary value problem for certain linear elliptic differential equations involving two small parameters

1967 • 6 citations

Asymptotic simplification of self-adjoint differential equations with a parameter

1966 • 5 citations

The Dirichlet problem for a thin rectangle

1967 • 5 citations

Equivalent classes of singular perturbation problems

1965 • 5 citations

ON THE ASYMPTOTIC SOLUTIONS OF A CLASS OF ORDINARY DIFFERENTIAL EQUATIONS OF THE FOURTH ORDER

1987 • 4 citations

Singular Perturbation Problems

2009 • 4 citations

Boundary layers for almost characteristic boundaries

1968 • 4 citations

Perturbations singulières relatives au problème de Dirichlet dans un demi-espace

1964 • 4 citations

Forced Oscillations of the Generalized Liénard Equation

1967 • 4 citations

The Nature of Solutions of a Rayleigh-Type Forced Vibration Equation with a Large Coefficient of Damping

1953 • 3 citations

The second initial-boundary-value problem for a linear parabolic equation with a small parameter.

1968 • 3 citations

Über eine asymptotische Darstellung der Lösung eines Systems von Differentialgleichungen, welche von zwei Parametern abhängen, und eine Anwendung auf spezielle Differentialgleichungen zweiter Ordnung

1961 • 3 citations

Asymptotic solutions of Whittaker's differential equation as the moduli of the independent variable and two parameters tend to infinity

1963 • 2 citations

On the Single First-Order Partial Differential Equation with a Small Parameter

1966 • 2 citations

On the asymptotic solution of multi-point boundary value problems

1970 • 2 citations

A singular perturbation method

1966 • 1 citations

The asymptotic form of the solution to the cauchy problem for an integro-differential equation with a small parameter

1967 • 1 citations

V. SINGULAR PERTURBATIONS OF A VAN DER POL EQUATION

1950 • 1 citations

Deleted Work

1955 • 0 citations