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1999 | 72 | 3 | 273-284
Tytuł artykułu

Disconjugacy and disfocality criteria for second order singular half-linear differential equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We establish Vallée Poussin type disconjugacy and disfocality criteria for the half-linear second order differential equation
$u'' = p(t)|u|^α |u'|^{1-α} sgn u + g(t)u'$,
where α ∈ (0,1] and the functions $p,g ∈ L_{loc}(a,b)$ are allowed to have singularities at the end points t = a, t = b of the interval under consideration.
Rocznik
Tom
72
Numer
3
Strony
273-284
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-05-12
Twórcy
  • Mathematical Institute, Czech Academy of Sciences, Žižkova 22, CZ-616 62 Brno, Czech Republic
  • Department of Mathematics, Masaryk University, Janáčkovo nám. 2a, CZ-662 95 Brno, Czech Republic
Bibliografia
  • [1] J. Andres, On the criterion of de la Vallée Poussin, Publ. Math. Debrecen 45 (1994), 145-152.
  • [2] T. Chantladze, N. Kandelaki and A. Lomtatidze, On zeros of solutions of second order singular half-linear equations, Mem. Differential Equations Math. Phys. 17 (1999), 127-154.
  • [3] J. H. E. Cohn, On an oscillation criterion of de la Vallée Poussin, Quart. J. Math. Oxford Ser. (2) 39 (1988), 173-174.
  • [4] O. Došlý, A remark on conjugacy of half-linear second order differential equations, Math. Slovaca, to appear.
  • [5] O. Došlý, Oscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 28 (1998), 507-521.
  • [6] A. Elbert and T. Kusano, Principal solutions of nonoscillatory half-linear differential equations, Adv. Math. Sci. Appl. 18 (1998), 745-759.
  • [7] A. Elbert, T. Kusano and T. Tanigawa, An oscillatory half-linear differential equation, Arch. Math. (Brno) 33 (1997), 165-172.
  • [8] B. J. Harris, On an oscillation criterion of Cohn, Quart. J. Math. Oxford Ser. (2) 42 (1991), 309-313.
  • [9] P. Hartman and A. Wintner, On an oscillation criterion of de la Vallée Poussin, Quart. Appl. Math. 13 (1955), 330-332.
  • [10] I. T. Kiguradze and A. G. Lomtatidze, On certain boundary value problems for second order linear ordinary differential equations with singularities, J. Math. Anal. Appl. 101 (1984), 325-347.
  • [11] I. T. Kiguradze and B. L. Shekhter, Singular boundary value problems for second order ordinary differential equations, Itogi Nauki i Tekh. Ser. Sovrem. Probl. Mat. 30 (1987), 105-201 (in Russian); English transl.: J. Soviet Math. 43 (1988), 2340-2417.
  • [12] T. Kusano and M. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Math. Hungar. 76 (1997), 81-99.
  • [13] T. Kusano, Y. Naito and A. Otaga, Strong oscillation and nonoscillation of quasilinear differential equations of second order, Differential Equations Dynam. Systems 2 (1994), 1-10.
  • [14] H. J. Li, Oscillation criteria for half-linear second order differential equations, Hiroshima Math. J. 25 (1995), 571-583.
  • [15] H. J. Li and C. C. Yeh, Sturmian comparison theorem for half-linear second order differential equations, Proc. Roy. Soc. Edinburgh 125A (1996), 1193-1204.
  • [16] A. Lomtatidze, Oscillation and nonoscillation of Emden-Fowler type equation of second order, Arch. Math. (Brno) 32 (1996), 181-193.
  • [17] J. D. Mirzov, On some analogs of Sturm's and Kneser's theorems for nonlinear systems, J. Math. Anal. Appl. 53 (1976), 418-425.
  • [18] J. D. Mirzov, Asymptotic Properties of Nonlinear Nonautonomous Systems of Ordinary Differential Equations, Adygeja, Majkop, 1994.
  • [19] Z. Opial, Sur une inégalité de Ch. de la Vallée Poussin dans la théorie de l'équation différentielle linéaire du second ordre, Ann. Polon. Math. 6 (1959), 81-91.
  • [20] G. Sansone, Equazioni differenziali nel campo reale, parte prima, Zanichelli, Bologna, 1948.
  • [21] Ch. de la Vallée Poussin, Sur l'équation différentielle linéaire du second ordre. Détermination d'une intégrale par deux valeurs assignés. Extension aux équations d'ordre n, J. Math. Pures Appl. 8 (1929), 125-144.
  • [22] D. Willet, Generalized de la Vallée Poussin disconjugacy test for linear differential equations, Canad. Math. Bull. 14 (1971), 419-428.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv72z3p273bwm
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