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

Svatoslav Staněk

Annales Polonici Mathematici (1993)

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

Abstract

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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.

How to cite

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Svatoslav 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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  1. [1] F. A. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. Zbl0249.35043
  2. [2] F. A. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, ibid. 54 (1974), 373-392. Zbl0293.35039
  3. [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968. 
  4. [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. [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. [6] W. Okrasiński, On a nonlinear ordinary differential equation. Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038
  7. [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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