Construction of two-sided approximations to positive solutions of semilinear Navier problem

Abstract

A homogeneous Navier problem for a semilinear four-order elliptic equations has been considered. To construct two-way approximations to a positive solution of this problem the methods of the theory of semi-ordered spaces, in particular, the results of V.I. Opoĭcev on the solvability of operator equations with a heterotone operator has been used. The work and the effectiveness of the developed method have been demonstrated by a computational experiment for the problem with power non-linearity.