# On positive solutions of a class of second order nonlinear differential equations on the halfline

Annales Polonici Mathematici (1995)

- Volume: 62, Issue: 2, page 123-142
- ISSN: 0066-2216

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topSvatoslav Staněk. "On positive solutions of a class of second order nonlinear differential equations on the halfline." Annales Polonici Mathematici 62.2 (1995): 123-142. <http://eudml.org/doc/262632>.

@article{SvatoslavStaněk1995,

abstract = {The differential equation of the form $(q(t)k(u)(u^\{\prime \})^a)^\{\prime \} = f(t)h(u)u^\{\prime \}$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.},

author = {Svatoslav Staněk},

journal = {Annales Polonici Mathematici},

keywords = {nonlinear second order differential equation; nonnegative solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on the parameter; boundary value problem on a noncompact interval; Tikhonov-Schauder fixed point theorem; water percolation; existence; uniqueness; boundedness; continuous dependence; Tikhonov-Schauder fixed point theorems},

language = {eng},

number = {2},

pages = {123-142},

title = {On positive solutions of a class of second order nonlinear differential equations on the halfline},

url = {http://eudml.org/doc/262632},

volume = {62},

year = {1995},

}

TY - JOUR

AU - Svatoslav Staněk

TI - On positive solutions of a class of second order nonlinear differential equations on the halfline

JO - Annales Polonici Mathematici

PY - 1995

VL - 62

IS - 2

SP - 123

EP - 142

AB - The differential equation of the form $(q(t)k(u)(u^{\prime })^a)^{\prime } = f(t)h(u)u^{\prime }$, a ∈ (0,∞), is considered and solutions u with u(0) = 0 and (u(t))² + (u’(t))² > 0 on (0,∞) are studied. Theorems about existence, uniqueness, boundedness and dependence of solutions on a parameter are given.

LA - eng

KW - nonlinear second order differential equation; nonnegative solution; existence and uniqueness of solutions; bounded solution; dependence of solutions on the parameter; boundary value problem on a noncompact interval; Tikhonov-Schauder fixed point theorem; water percolation; existence; uniqueness; boundedness; continuous dependence; Tikhonov-Schauder fixed point theorems

UR - http://eudml.org/doc/262632

ER -

## References

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- [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
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- [5] P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Akademie-Verlag, Berlin, 1969.
- [6] 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.
- [7] W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038
- [8] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, Ann. Polon. Math. 57 (1992), 71-82. Zbl0774.34017
- [9] S. Staněk, Qualitative behavior of a class of second order nonlinear differential equations on the halfline, Ann. Polon. Math. 58 (1993), 65-83. Zbl0777.34027

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