Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
The differential equation of the form $(q(t)k(u)(u')^a)' = f(t)h(u)u'$, 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.
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
123-142
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-06-30
poprawiono
1994-11-20
Twórcy
autor
- Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 06 Olomouc, Czech Republic
Bibliografia
- [1] F. A. Atkinson and L. A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379.
- [2] F. A. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974), 373-392.
- [3] J. Bear, D. Zaslavsky and S. Irmay, Physical Principles of Water Percolation and Seepage, UNESCO, 1968.
- [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.
- [5] P. Natanson, Theorie der Funktionen einer reellen Veränderlichen, Akademie-Verlag, Berlin, 1969.
- [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.
- [7] W. Okrasiński, On a nonlinear ordinary differential equation, Ann. Polon. Math. 49 (1989), 237-245.
- [8] S. Staněk, Nonnegative solutions of a class of second order nonlinear differential equations, Ann. Polon. Math. 57 (1992), 71-82.
- [9] S. Staněk, Qualitative behavior of a class of second order nonlinear differential equations on the halfline, Ann. Polon. Math. 58 (1993), 65-83.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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