2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122311The paper presents theorems on the calculation of the index of a singular point and at the infinity of monotone type mappings. These theorems cover basic cases when the principal linear part of a mapping is degenerate. Applications of these theorems to proving solvability and nontrivial solvability of the Dirichlet problem for ordinary and partial differential equations are considered.9 pagesAnalysis of PDEs47H11; 34B15; 35G25text