ArticleOriginal scientific text
Title
Qualitative behavior of a class of second order nonlinear differential equations on the halfline
Authors 1
Affiliations
- Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 38, 772 00 Olomouc, Czechoslovakia
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.
Keywords
nonlinear differential equation, nonnegative solution, nonpositive solution, existence and uniqueness of solutions, bounded solution, dependence of solutions on a parameter, boundary value problem
Bibliography
- F. A. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379.
- F. A. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, ibid. 54 (1974), 373-392.
- J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
- 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.
- 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.
- W. Okrasiński, On a nonlinear ordinary differential equation. Ann. Polon. Math. 49 (1989), 237-245.
- S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, ibid. 57 (1992), 71-82.
Pages:
65-83
Main language of publication
English
Received
1992-03-26
Accepted
1992-07-07
Published
1993
Exact and natural sciences