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

Annales Polonici Mathematici (1993)

- Volume: 58, Issue: 1, page 65-83
- ISSN: 0066-2216

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topSvatoslav Staněk. "Qualitative behavior of a class of second order nonlinear differential equations on the halfline." Annales Polonici Mathematici 58.1 (1993): 65-83. <http://eudml.org/doc/262454>.

@article{SvatoslavStaněk1993,

abstract = {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.},

author = {Svatoslav Staněk},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear differential equation; nonnegative solution; nonpositive solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on a parameter; boundary value problem; existence-uniqueness theorems; qualitative properties; nonlinear problem; boundedness; monotony},

language = {eng},

number = {1},

pages = {65-83},

title = {Qualitative behavior of a class of second order nonlinear differential equations on the halfline},

url = {http://eudml.org/doc/262454},

volume = {58},

year = {1993},

}

TY - JOUR

AU - Svatoslav Staněk

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

JO - Annales Polonici Mathematici

PY - 1993

VL - 58

IS - 1

SP - 65

EP - 83

AB - 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.

LA - eng

KW - nonlinear differential equation; nonnegative solution; nonpositive solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on a parameter; boundary value problem; existence-uniqueness theorems; qualitative properties; nonlinear problem; boundedness; monotony

UR - http://eudml.org/doc/262454

ER -

## References

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- [2] F. A. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, ibid. 54 (1974), 373-392. Zbl0293.35039
- [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
- [4] J. Goncerzewicz, H. Marcinkowska, W. Okrasiński and K. Tabisz, On the percolation of water from a cylindrical reservoir into the surrounding soil, Zastos. Mat. 16 (1978), 249-261. Zbl0403.76078
- [5] W. Okrasiński, Integral equations methods in the theory of the water percolation, in: Mathematical Methods in Fluid Mechanics, Proc. Conf. Oberwolfach, 1981, Band 24, P. Lang, Frankfurt/M, 1982, 167-176.
- [6] W. Okrasiński, On a nonlinear ordinary differential equation. Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038
- [7] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, ibid. 57 (1992), 71-82. Zbl0774.34017

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