# Nonnegative solutions of a class of second order nonlinear differential equations

Annales Polonici Mathematici (1992)

- Volume: 57, Issue: 1, page 71-82
- ISSN: 0066-2216

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topS. Staněk. "Nonnegative solutions of a class of second order nonlinear differential equations." Annales Polonici Mathematici 57.1 (1992): 71-82. <http://eudml.org/doc/262270>.

@article{S1992,

abstract = {
A differential equation of the form
(q(t)k(u)u')' = λf(t)h(u)u'
depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.
},

author = {S. Staněk},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear ordinary differential equation; nonnegative solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on a parameter; boundary value problem; positive solutions; existence of a maximal solution; minimal solution; boundedness; uniqueness},

language = {eng},

number = {1},

pages = {71-82},

title = {Nonnegative solutions of a class of second order nonlinear differential equations},

url = {http://eudml.org/doc/262270},

volume = {57},

year = {1992},

}

TY - JOUR

AU - S. Staněk

TI - Nonnegative solutions of a class of second order nonlinear differential equations

JO - Annales Polonici Mathematici

PY - 1992

VL - 57

IS - 1

SP - 71

EP - 82

AB -
A differential equation of the form
(q(t)k(u)u')' = λf(t)h(u)u'
depending on the positive parameter λ is considered and nonnegative solutions u such that u(0) = 0, u(t) > 0 for t > 0 are studied. Some theorems about the existence, uniqueness and boundedness of solutions are given.

LA - eng

KW - nonlinear ordinary differential equation; nonnegative solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on a parameter; boundary value problem; positive solutions; existence of a maximal solution; minimal solution; boundedness; uniqueness

UR - http://eudml.org/doc/262270

ER -

## References

top- [1] F. V. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. Zbl0249.35043
- [2] F. V. 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 am Main 1982, 167-176.
- [6] W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038

## Citations in EuDML Documents

top- Xingbao Wu, Qualitative investigation of nonlinear differential equations describing infiltration of water
- Svatoslav Staněk, Qualitative behavior of a class of second order nonlinear differential equations on the halfline
- Svatoslav Staněk, On positive solutions of a class of second order nonlinear differential equations on the halfline

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