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Qualitative investigation of nonlinear differential equations describing infiltration of water

100%

Wu X.

Annales Polonici Mathematici

1995

tom 61

nr 1

39-57

A nonlinear differential equation of the form (q(x)k(x)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(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.

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On the asymptotic behaviors of solutions to nonlinear differential equations of second order

100%

Tunc C., Ayhan T.

Commentationes Mathematicae

2015

tom 55

nr 1

We study the asymptotic behavior of solutions to a nonlinear differential equation of the second order whose coefficient of nonlinearity is a bounded function for arbitrarily large values of \(x\) in \(R\). We obtain certain sufficient conditions which guarantee boundedness of solutions, their convergence to zero as \(x\rightarrow \infty\) and their unboundedness.

Qualitative behavior of a class of second order nonlinear differential equations on the halfline

75%

Staněk S.

Annales Polonici Mathematici

1993

tom 58

nr 1

65-83

A differential equation of the form (q(t)k(u)u')' = F(t,u)u' is considered and solutions u with u(0) = 0 are studied on the halfline [0,∞). Theorems about the existence, uniqueness, boundedness and dependence of solutions on a parameter are given.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Commentationes Mathematicae

1 Ayhan T.

1 Staněk S.

1 Tunc C.

1 Wu X.

1 2015

1 1995

1 1993

Wyniki wyszukiwania

Qualitative investigation of nonlinear differential equations describing infiltration of water

On the asymptotic behaviors of solutions to nonlinear differential equations of second order

Qualitative behavior of a class of second order nonlinear differential equations on the halfline