Abstract:
The article deals with the existence of a generalized solution for the second order nonlinear differential
equation in an unbounded domain. Intermediate and lower coefficients of the equation depends on the
required function and considered smooth. The novelty of the work is that we prove the solvability of a
nonlinear singular equation with the leading coefficient not separated from zero. In contrast to the works
considered earlier, the leading coefficient of the equation can tend to zero, while the intermediate coefficient
tends to infinity and does not depend on the growth of the lower coefficient. The result obtained formulated
in terms of the coefficients of the equation themselves; there are no conditions on any derivatives of these
coefficients.
