论文信息 - A Second Order Differential Equation with Singular Solutions

A Second Order Differential Equation with Singular Solutions

where k is a large constant and b and X are constants. While only a sketch of the method of CArtwright and Littlewood has appeared, the authors state that their proof is difficult. Here we shall consider an equation which exhibits the same singular behavior but for which the proof is considerably simplified by an artifice (described in ?2). A summary of our results has already appeared [9]. We consider

N. Levinson | Norman Levinson

[1] N. Levinson. A Simple Second Order Differential Equation with Singular Motions. , 1948, Proceedings of the National Academy of Sciences of the United States of America.

[2] J. E. Littlewood,et al. On Non‐Linear Differential Equations of the Second Order: I. the Equation y¨ − k(1‐y2)y˙ + y = bλk cos(λl + α), k Large , 1945 .

[3] N. Levinson,et al. Transformation Theory of Non-Linear Differential Equations of the Second Order , 1944 .

[4] George D. Birkhoff. Sur le problème restreint des trois corps (second mémoire) , 1936 .

[5] Gaetano Scorza. Sulle algebre pseudonulle di ordine massimo , 1935 .

[6] G. D. Birkhoff. Sur quelques courbes fermées remarquables , 1932 .

[7] George D. Birkhoff,et al. Surface transformations and their dynamical applications , 1922 .

[8] Harold Marston Morse. Recurrent geodesics on a surface of negative curvature , 1921 .

[9] J. Hadamard,et al. Les surfaces a courbures opposees et leurs lignes geodesique , 1898 .