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Qualitative investigation of nonlinear differential equations describing infiltration of water. (English) Zbl 0827.34012

Water filtration problems modeled by nonlinear second-order ODE’s of the kind \((q(x)k(u)u')= \lambda F(x, u, u')\), \(x> 0\), \(\lambda> 0\) are discussed. Existence, boundedness, uniqueness and dependence of the solution on the paramter \(\lambda\) are established.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
45G10 Other nonlinear integral equations
34C11 Growth and boundedness of solutions to ordinary differential equations
76S05 Flows in porous media; filtration; seepage
34A34 Nonlinear ordinary differential equations and systems
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