Selected Papers of Norman Levinson

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Product Details

  • ISBN-13: 9781461253433
  • Publisher: Birkhauser Verlag
  • Publication date: 12/31/2013
  • Series: Contemporary Mathematicians Series
  • Edition description: Softcover reprint of the original 1st ed. 1998
  • Pages: 536
  • Product dimensions: 7.00 (w) x 10.00 (h) x 1.18 (d)

Table of Contents

— Volume 1.- I. Stability and Asymptotic Behavior of Solutions of Ordinary Differential Equations.- Commentary on [L 31] and [L 36].- [L 20] The Growth of the Solutions of a Differential Equation (1941).- [L 24] The Growth of the Solutions of a Differential Equation (1942).- [L 31] The Asymptotic Behavior of a System of Linear Differential Equations (1946).- [L 36] The Asymptotic Nature of Solutions of Linear Systems of Differential Equations (1948).- [L 40] On Stability of Non-Linear Systems of Differential Equations (1949).- [L 68] On u? + (1 + ? g(x)) u = 0 for ?0? | g(x)|dx < ? (1959).- II. Nonlinear Oscillations and Dynamical Systems.- Commentary on [L 29], [L 38] and [L 47].- [L 23] A General Equation for Relaxation Oscillations (1942).- [L 25] On the Existence of Periodic Solutions for Second Order Differential Equations with a Forcing Term (1943).- [L 29] Transformation Theory of Non-Linear Differential Equations of the Second Order (1944) and Correction (1948).- [L 38] A Second Order Differential Equation with Singular Solutions (1949).- [L 47] Small Periodic Perturbations of an Autonomous System with a Stable Orbit (1950).- [L 52] Forced Periodic Solutions of a Stable Non-Linear System of Differential Equations (1951).- [L 57] On the Non-Uniqueness of Periodic Solutions for an Asymmetric Lienard Equation (1952).- III. Inverse Problems for Sturm-Liouville and Schrödinger Operators.- Commentary on [L 41], [L 43] and [L 58].- [L 41] On the Uniqueness of the Potential in a Schrödinger Equation for a Given Asymptotic Phase (1949).- [L 42] Determination of the Potential from the Asymptotic Phase (1949).- [L 43] The Inverse Sturm-Liouville Problem (1949).- [L 58] Certain Explicit Relationships between Phase Shift and Scattering Potential (1953).- IV. Eigenfunction Expansions and Spectral Theory for Ordinary Differential Equations.- Commentary on [L 49], [L 51], and [L 59].- [L 39] Criteria for the Limit-Point Case for Second Order Linear Differential Operators (1949).- [L 49] A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations (1951).- [L 50] Addendum to “A Simplified Proof of the Expansions Theorem for Singular Second Order Linear Differential Equations” (1951).- [L 51] On the Nature of the Spectrum of Singular Second Order Linear Differential Equations (1951).- [L 53] The L-Closure of Eigenfunctions Associated with Selfadjoint Boundary Value Problems (1952).- [L 59] The Expansion Theorem for Singular Self-Adjoint Linear Differential Operators (1954).- [L 65] Transform and Inverse Transform Expansions for Singular Self-Adjoint Differential Operators (1958).- V. Singular Perturbations of Ordinary and Partial Differential Equations.- Commentary on [L 45], [L 48], [L 60], [L 62], [L 63], [L 67], [L 56] and [L 46].- [L 45] Perturbations of Discontinuous Solutions of Non-Linear Systems of Differential Equations (1950).- [L 48] An Ordinary Differential Equation with an Interval of Stability, a Separation Point, and an Interval of Instability (1950).- [L 60] Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation (1954).- [L 62] Periodic Solutions of Singularly Perturbed Systems (1955).- [L 56] A Boundary Value Problem for a Nonlinear Differential Equation with a Small Parameter (1952).- [L 63] A Boundary Value Problem for a Singularly Perturbed Differential Equation (1955).- [L 67] A Boundary Value Problem for a Singularly Perturbed Differential Equation (1958).- [L 46] The First Boundary Value Problem for ??u +A(x,y)ux + B(x,y)uy + C(x, y)u = D(x,y) for small ? (1950).- VI. Elliptic Partial Differential Equations.- Commentary on [L 75], [L 78], [L87].- [L 75] Positive Eigenfunctions for ?u + ?f(u) = 0 (1962).- [L 78] Dirichlet Problem for ?u = f(P, u) (1963).- [L 87] One-Sided Inequalities for Elliptic Differential Operators (1965).- VII. Integral Equations.- Commentary on [L 73].- [L 32] On the Asymptotic Shape of the Cavity Behind an Axially Symmetric Nose Moving Through an Ideal Fluid (1946).- [L 73] A Nonlinear Volterra Equation Arising in the Theory of Superfluidity (1960).- [L 89] Simplified Treatment of Integrals of Cauchy Type, the Hilbert Problem and Singular Integral Equations. Appendix: Poincar é-Bertrand Formula (1965).
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