Convergence results for unbounded solutions of first order non-linear differential-functional equations
Volume 64 / 1996
Annales Polonici Mathematici 64 (1996), 1-16
DOI: 10.4064/ap-64-1-1-16
Abstract
We consider the Cauchy problem in an unbounded region for equations of the type either $D_{t}z(t,x) = f(t,x,z(t,x),z_{(t,x)},D_{x}z(t,x))$ or $D_{t}z(t,x)= f(t,x,z(t,x),z,D_{x}z(t,x))$. We prove convergence of their difference analogues by means of recurrence inequalities in some wide classes of unbounded functions.
