5 papers
Global solution curves for first order periodic problems, with applications
Philip Korman, Dieter S. Schmidt
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for periodic problems of first order. T…
Infinitely many solutions and asymptotics for resonant oscillatory problems
Philip Korman, Dieter S. Schmidt
For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in , we show the existence of infinitely many solutions…
Computation and analysis of global solution curves for super-critical equations
Philip Korman, Dieter S. Schmidt
We study analytical and computational aspects for Dirichlet problem on the unit ball : in , modeled on the equation \[ Δu +λ\left(u^p+u^q \right)=0, \;\; \mbox{in $…
Continuation of global solution curves using global parameters
Philip Korman, Dieter S. Schmidt
This paper provides both the theoretical results and numerical calculations of global solution curves, by continuation in global parameters. Each point on the solution curves is co…
Bounding Solutions of a Forced Oscillator
K. R. Meyer, D. S. Schmidt
Our proof is based on a generalization of action-angle variables, a convergent Lie transformation, and Moser's invariant curve theorem. As an overall outline we give a quick proof…