Nonnegative solutions of a class of second order nonlinear differential equations

S. Staněk

Annales Polonici Mathematici (1992)

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

Abstract

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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.

How to cite

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S. 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

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  1. [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. [2] F. V. 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 am Main 1982, 167-176. 
  6. [6] W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245. Zbl0685.34038

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