Interval Arithmetic and Solvability of Boundary Value Problems

Jiří Benedikt

Katedra matematiky
Západočeská univerzita v Plzni
Czech Republic

Abstract

We use interval arithmetic implemented in Mathematica to prove existence/nonexistence of solutions of a Dirichlet boundary value problem for the strongly nonlinear second-order ordinary differential equation

-(|u'((|)^(p-2))u')'=λ|u((|)^(p-2))u+f

where λ∈R is a spectral parameter, p>1 is a constant, and f is a given function.