Solvability of nonlinear equations in a cone of a banach space

The solvability conditions for the equation Tu+F(u)=0 are found in the case where the operator T+F′(u)]⁻¹ exists only for u∈K, where K is a cone in a Banach space X. An application concerning the solvability of boundary-value problems for systems of second-order differential equations is provided. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 248, 1998, pp. 225–230. Translated by L. Yu. Kolotilina.