MATHEMATICAL APPLICATIONS OF THE INDUCTION METHOD IN THE THEORY OF ABSTRACT STATIONARY EQUATIONS

Abstract

We study abstract systems of stationary inequalities of the following type:

\[
\sum_{1\leq j\leq m} a_{ij}\widetilde{K}_{\tau_{ij}}(x_j)\leq N_i,
\qquad 1\leq i\leq t,
\]

where \(m,t,N_i\) (\(1\leq i\leq t\)), \(a_{ij}\) (\(1\leq i\leq t,\ 1\leq j\leq m\)) are the elements of the set \(Z_+\) - the set of natural numbers.

In this article we formulate and prove theorems about the solutions of an abstract stationary equation \(\widetilde{K}_{\eta}(x)=r\), \(r\in Z_+\), and observe [7] estimates for the number of solutions of (1).