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A nonlinear differential equation of the form (q(x)k(u)u ) = F (x, u, u ) arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(u)u ) = λF (x, u, u ). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established. 1991 Mathematics Subject Classification: 34B15, 45G10, 34C11, 34A34.doi:10.4064/ap-61-1-39-57 fatcat:xgkusfwd6rbptgg2vy3vczc43i