Pacific Journal of Mathematics · 1967 · 93 citations · 22 references
Natural SciencesMathematicsPhysicsDifferential EquationsNuclear PhysicsTheoretical PhysicsBoundary ConditionsBoundary-value ProblemsEigenvalue ProblemsPartial Differential EquationsAsymptotic TheoryBoundary Value Eigenvalue ProblemsEigenvalue Boundary-value ProblemsNonlinear Differential-algebraic EquationsNonlinear Partial Differential EquationsNonlinear Variational ProblemsVariational Problems
For certain functions /, positive in (0, oo) and continuous in [0, oo), the partial differential equation x = xxf(x 2 ) has spherically symmetric solutions x n (t), n -1, 2, , which vanish at zero, infinity and n -1 distinct values in (0, oo). This and similar existence theorems for the ordinary differential equation V -V + yF(y 2 , 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.
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