Selected Works of Norman Levinson

- 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] (with Mary L. Boas and R. P. Boas, Jr.), 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] (with R. R. D. Kemp), On $$u\prime \prime + \left( {1 + \lambda g\left( x \right)} \right)u = 0$$ for $$\int_0^\infty {\left| {g\left( x \right)} \right|dx}(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] (with E. A. Coddington), On the Nature of the Spectrum of Singular Second Order Linear Differential Equations (1951).- [L 53] TheL-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] (with J. J. Levin), Singular Perturbations of Non-Linear Systems of Differential Equations and an Associated Boundary Layer Equation (1954).- [L 62] (with L. Flatto), Periodic Solutions of Singularly Perturbed Systems (1955).- [L 56] (with E. A. Coddington), ABoundary Value Problem for a Nonlinear Differential Equation with a Small Parameter (1952).- [L 63] (with S. Haber), 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$$ \in \Delta + {\rm A}\left( {x,y} \right){u_x} + {\rm B}\left( {x,y} \right){u_y} + C\left( {x,y} \right)u = D\left( {x,y} \right)$$ for small ? (1950).- VI. Elliptic Partial Differential Equations.- Commentary on [L 75], [L 78], [L 87].- [L 75] Positive Eigenfunctions for $$\Delta u + \lambda f\left( u \right) = 0$$ (1962).- [L 78] Dirichlet Problem for $$\Delta u = f\left( {{\rm P},u} \right)$$ (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: Poincare-Bertrand Formula (1965).