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.
@article{bwmeta1.element.bwnjournal-article-apmv58z1p65bwm,
author = {Svatoslav Stan\v ek},
title = {Qualitative behavior of a class of second order nonlinear differential equations on the halfline},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {65-83},
zbl = {0777.34027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p65bwm}
}
Svatoslav Staněk. Qualitative behavior of a class of second order nonlinear differential equations on the halfline. Annales Polonici Mathematici, Tome 58 (1993) pp. 65-83. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z1p65bwm/
[000] [1] F. A. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. | Zbl 0249.35043
[001] [2] F. A. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, ibid. 54 (1974), 373-392. | Zbl 0293.35039
[002] [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
[003] [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. | Zbl 0403.76078
[004] [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.
[005] [6] W. Okrasiński, On a nonlinear ordinary differential equation. Ann. Polon. Math. 49 (1989), 237-245. | Zbl 0685.34038
[006] [7] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, ibid. 57 (1992), 71-82. | Zbl 0774.34017