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The solvability for a singularly perturbed quasi-linear differential system of second order. (English) Zbl 1240.34271
Summary: We consider a class of quasi-linear differential systems. By using the boundary layer method, Green’s formula and the theory of differential inequalities, the condition for the solvability of the two points problem for the singularly perturbed differential system of second order is obtained.
34E15 Singular perturbations, general theory for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34A40 Differential inequalities involving functions of a single real variable
34B27 Green’s functions for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations