Vol. 22, No. 3, 1967

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ISSN: 0030-8730
Boundary value problems for a class of nonlinear differential equations

Gerald H. Ryder

Vol. 22 (1967), No. 3, 477–503
Abstract

For certain functions f, positive in (0,) and continuous in [0,), the partial differential equation Δx = xxf(x2) has spherically symmetric solutions xn(t),n = 1,2, , which vanish at zero, infinity and n 1 distinct values in (0,). This and similar existence theorems for the ordinary differential equation ÿy + yF(y2,t) = 0 are proved by way of variational problems and the solutions are thus characterized by associated “eigenvalues”. The asymptotic behavior of these eigenvalues is studied and some numerical data on the solutions is furnished for special cases of the above equations which are of interest in nuclear physics.

Mathematical Subject Classification
Primary: 34.36
Milestones
Received: 9 July 1965
Revised: 9 July 1966
Published: 1 September 1967
Authors
Gerald H. Ryder