# Article

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Keywords:
Singular ordinary differential equation of the second order; lower and upper functions; time singularities; unbounded domain; homoclinic solution
Summary:
The paper investigates singular nonlinear problems arising in hydrodynamics. In particular, it deals with the problem on the half-line of the form $(p(t)u^{\prime }(t))^{\prime } = p(t)f(u(t)),$ $u^{\prime }(0) = 0,\quad u(\infty ) = L.$ The existence of a strictly increasing solution (a homoclinic solution) of this problem is proved by the dynamical systems approach and the lower and upper functions method.
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