The differential equation of the form , 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.
@article{bwmeta1.element.bwnjournal-article-apmv62z2p123bwm, author = {Svatoslav Stan\v ek}, title = {On positive solutions of a class of second order nonlinear differential equations on the halfline}, journal = {Annales Polonici Mathematici}, volume = {62}, year = {1995}, pages = {123-142}, zbl = {0839.34006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv62z2p123bwm} }
Svatoslav Staněk. On positive solutions of a class of second order nonlinear differential equations on the halfline. Annales Polonici Mathematici, Tome 62 (1995) pp. 123-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv62z2p123bwm/
[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, Arch. Rational Mech. Anal. 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] P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Akademie-Verlag, Berlin, 1969.
[005] [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.
[006] [7] W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245. | Zbl 0685.34038
[007] [8] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, Ann. Polon. Math. 57 (1992), 71-82. | Zbl 0774.34017
[008] [9] S. Staněk, Qualitative behavior of a class of second order nonlinear differential equations on the halfline, Ann. Polon. Math. 58 (1993), 65-83. | Zbl 0777.34027