On positive solutions of a class of second order nonlinear differential equations on the halfline

• Autorzy: Svatoslav Staněk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

nonlinear second order differential equation   nonnegative solution   existence and uniqueness of solutions   bounded solution   dependence of solutions on the parameter   boundary value problem on a noncompact interval   Tikhonov-Schauder fixed point theorem  

Kategorie tematyczne

• 34B15: Nonlinear boundary value problems
• 34C11: Growth, boundedness
• 45G10: Other nonlinear integral equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1995
• Tom: 62
• Numer: 2
• Strony: 123-142

Daty

wydano

1995

otrzymano

1994-06-30

poprawiono

1994-11-20

Twórcy

autor

Svatoslav Staněk

• 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.