A BOUNDARY VALUE PROBLEM ON A HALF-LINE FOR DIFFERENTIAL EQUATIONS WITH INDEFINITE WEIGHT

TitleA BOUNDARY VALUE PROBLEM ON A HALF-LINE FOR DIFFERENTIAL EQUATIONS WITH INDEFINITE WEIGHT
Publication TypeJournal Article
Year of Publication2011
AuthorsDOSLA, ZUZANA, MARINI, MAURO, MATUCCI, SERENA
Secondary TitleCommunications in Applied Analysis
Volume15
Issue3
Start Page341
Pagination352
Date Published08/2011
Type of Workscientific: mathematics
ISSN1083–2564
AMS34B18, 34B40, 34C11.
Abstract
he boundary value problem on the half-line for the second order differential equation with general Φ-Laplacian
is considered, where a, b are continuous functions on [0, ∞), a is positive and b can change its sign. The cases of regular variation, slow variation, and rapid variation of the inverse function Φ∗ of Φ are considered. Some applications of the main results complete the paper.
URLhttp://www.acadsol.eu/en/articles/15/3/6.pdf
Short TitleA BOUNDARY VALUE PROBLEM ON A HALF-LINE
Refereed DesignationRefereed
Full Text
REFERENCES
[1] R. P. Agarwal, S. R. Grace, D. O’Regan, Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, Kluwer Academic Publishers, Dordrecht, 2002.
[2] N. H. Bingham, C. M. Goldie, J. L. Teugels, Regular variation, Encyclopedia of Mathematics and its Applications 27, Cambridge University Press, Cambridge, 1987.
[3] M. Cecchi, Z. Dosla, I. T. Kiguradze, M. Marini, On nonnegative solutions of singular boundary value problems for Emden-Fowler type differential systems, Differential Integral Equations 20 (2007), 1081–1106.
[4] M. Cecchi, Z. Dosla, M. Marini, Monotone solutions of two-dimensional nonlinear functional differential systems, Dynam. Systems Appl. 17 (2008), 595–608.
[5] M. Cecchi, Z. Dosla, M. Marini, On second order differential equations with nonhomogeneous Phi-Laplacian, Bound. Value Probl. 2010, Article ID 875675, 1–17.
[6] M. Cecchi, Z. Dosla, M. Marini, Asymptotic problems for differential equation with bounded Phi-Laplacian, Electron. J. Qual. Theory Differ. Equ. 9 (2009), 1–18.
[7] M. Cecchi, Z. Dosla, M. Marini, I. Vrkoc, Integral conditions for nonoscillation of second order nonlinear differential equations, Nonlinear Anal. T.M.A. 64 (2006), 1278–1289.
[8] Z. Dosla, M. Marini, S. Matucci, On some boundary value problems for second order nonlinear differential equations, to appear on Math. Bohem.
[9] A. Elbert, T. Kusano, Oscillation and nonoscillation theorems for a class of second order quasilinear differential equations, Acta Math. Hungar. 56 (1990), 325–336.
[10] J. Jaros, T. Kusano, T. Tanigawa, Nonoscillation theory for second order half-linear differential equations in the framework of regular variation, Results Math. 43 (2003), 129–149.
[11] M. J. Karamata, Sur un mode de croissance reguliere des functions, Mathematica (Cluj) 4 (1930), 38–53.
[12] M. J. Karamata, Sur un mode de croissance reguliere. Theoremes fondamentaux, Bull. Soc. Math. France. 61 (1933), 55–62.
[13] I. T. Kiguradze, A. Chanturia, Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations, Mathematics and its Applications (Soviet Series) 89, Kluwer Academic Publishers Group, Dordrecht, 1993.
[14] T. Kusano, V. Maric, Slowly varying solutions of functional differential equations with retarded and advanced arguments, Georgian Math. J. 14 (2007), 301–314.
[15] T. Kusano, V. Maric, T. Tanigawa, Regularly varying solutions of generalized Thomas-Fermi equations, Bull. Cl. Sci. Math. Nat. Sci. Math. 34 (2009), 43–73.
[16] W. T. Li, S. S. Cheng, Limit behaviours of non-oscillatory solutions of a pair of coupled nonlinear differential equations, Proc. Edinb. Math. Soc. 43 (2000), 457–473.
[17] V. Maric, Regular variation and differential equations, Lect. Notes Math. 1726, Springer-Verlag, Berlin, 2000.
[18] J. D. Mirzov, Asymptotic properties of solutions of the systems of nonlinear nonautonomous ordinary differential equations, (Russian), Maikop, Adygeja Publ., 1993. English translation: Folia Fac. Sci. Natur. Univ. Masaryk Brun. Math. 14, 2004.
[19] J. Sugie, M. Onitsuka, A non-oscillation theorem for nonlinear differential equations with p-Laplacian, Proc. Roy. Soc. Edinburgh Sect. A. 136 (2006), 633–647.