On mildly nonlinear partial difference equations of elliptic type

Abstract

The use of t he fini te d ifferences met hod is in solving t he boundar y value problem of t he first kind for t he nonlinear elli ptic equation A</ > = F (X,y,</>, </>., cf>u) is justified by first showing t hat t h e problem of the corresp onding difference equat ion has a uniqu e solution, and t h en t hat t he solution of t he differe nce e quat ion tends t o that of t he different ial e quation when t he net uni t te nds t o zero. Also a numerical m cthod of t he Liebmann type for t he computa tion of t he solution of t he diffe re nce equat ion is deyeloped , and t hese result s are extended to more general n onlinear ellipt ic equat ions.