Geodesic
On asymptotic decaying solutions for a class of second order differential equations
Archivum mathematicum, Tome 35 (1999) no. 3, pp. 275-284 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The author considers the quasilinear differential equations \begin{gather} \left(r(t)\varphi (x^{\prime })\right)^{\prime }+ q(t)f(x)=0\,,\quad \quad t\ge a\\ \multicolumn{2}{l}{\text{and}}\\ \left(r(t)\varphi (x^{\prime })\right)^{\prime } + F(t,x)=\pm g(t)\,,\quad \quad t\ge a\,. \end{gather} By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.
The author considers the quasilinear differential equations \begin{gather} \left(r(t)\varphi (x^{\prime })\right)^{\prime }+ q(t)f(x)=0\,,\quad \quad t\ge a\\ \multicolumn{2}{l}{\text{and}}\\ \left(r(t)\varphi (x^{\prime })\right)^{\prime } + F(t,x)=\pm g(t)\,,\quad \quad t\ge a\,. \end{gather} By means of topological tools there are established conditions ensuring the existence of nonnegative asymptotic decaying solutions of these equations.
Classification : 34C11, 34D05
Keywords: nonoscillatory behavior; asymptotic decaying nonnegative solutions; fixed point theorem 
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Matucci, Serena. On asymptotic decaying solutions for a class of second order differential equations. Archivum mathematicum, Tome 35 (1999) no. 3, pp. 275-284. http://geodesic.mathdoc.fr/item/ARM_1999_35_3_a6/

[1] Atkinson F. V.: On second-order non-linear oscillations. Pacific J. Math. 5 (1955), 643–647. | MR | Zbl

[2] Cecchi M., Furi M., Marini M.: On continuity and compactness of some nonlinear operators associated with differential equations in noncompact intervals. Nonlinear Anal. TMA 9 (1985), 171–180. | MR | Zbl

[3] Cecchi M., Marini M., Villari G.: On some classes of continuable solutions of a nonlinear differential equation. J. Diff. Eq. 118 (1995), 403–419. | MR | Zbl

[4] Cecchi M., Marini M., Villari G.: Topological and variational approaches for nonlinear oscillation: an extension of a Bhatia result. In Proc. First World Congress Nonlinear Analysis, Walter de Gruyter, Berlin, 1996, 1505–1514. | MR | Zbl

[5] Cecchi M., Marini M., Villari G.: Oscillation criteria for second order differential equations. (to appear on NODEA), 1999.

[6] Del Pino M., Elgueta M., Manasevich R.: Generalizing Hartmann’s oscillation result for $(\vert x^{\prime }\vert ^{p-2} x^{\prime })^{\prime } + c(t) \vert x\vert ^{p-2} x =0, \, p>1$ . Houston J. Math. 17 (1991), 63–70. | MR

[7] Elbert Á.: A half-linear second order differential equation. In: Qualitative Theory of Differential Equations, volume 30 of Colloquia Math. Soc. Janos Bolyai, Szeged, 1979, 153–180. | MR

[8] Elbert Á.: Oscillation and nonoscillation theorems for some nonlinear ordinary differential equations. In: Ordinary and partial differential equations, volume 964 of Lect. Notes Math., Proc. 7th Conf., Dundee, Scotl., 1982, 187–212. | MR | Zbl

[9] Elbert Á., Kusano T.: Oscillation and non-oscillation theorems for a class of second order quasilinear differential equations. Acta Math. Hung. 56 (1990), 325–336. | MR

[10] Hartman P.: Ordinary Differential Equations. Birkhäuser, Boston, 2nd edition, 1982. | MR | Zbl

[11] Heidel J. W.: A nonoscillation theorem for a nonlinear second order differential equation. Proc. Amer. Math. Soc. 22 (1969), 485–488. | MR | Zbl

[12] Kiguradze I. T., Chanturia T. A.: Asymptotic properties of solutions of nonautonomous ordinary differential equations. Kluwer Academic Publishers, Dordrecht-Boston-London, 1992.

[13] Kusano T., Naito Y.: Oscillation and nonoscillation criteria for second order quasilinear differential equations. Acta Math. Hungar. 76 (1997), 81–99. | MR | Zbl

[14] Kusano T., Naito Y., Ogata Q.: Strong oscillation and nonoscillation of quasilinear differential equations of second order. J. Diff. Eq. and Dyn. Syst. 2 (1994), 1–10. | MR | Zbl

[15] Kusano T., Yoshida N.: Nonoscillation theorems for a class of quasilinear differential equations of second order. J. Math. Anal. Appl. 189 (1995), 115–127. | MR | Zbl

[16] Lomtatidze A.: Oscillation and nonoscillation of Emden-Fowler type equation of second order. Arch. Math. Brno 32 (1996), 181–193. | MR

[17] Mirzov J. D.: On the oscillation of a system of nonlinear differential equations. Differentsial’nye Uravneniya 9 (1973), 581–583, (in Russian). | MR

[18] Mirzov J. D.: On the question of oscillation of solutions of a system of nonlinear differential equations. Mat. Zametki 16 (1974), 571–576, (in Russian). | MR

[19] Mirzov J. D.: On some analogs of Sturm’s and Kneser’s theorems for nonlinear systems. J. Math. Anal. Appl. 53 (1976), 418–425. | MR | Zbl

[20] Mirzov J. D.: On the oscillation of solutions of a system of differential equations. Math. Zametki 23 (1978), 401–404, (in Russian). | MR

[21] Mirzov J. D.: Asymptotic properties of the solutions of the system of nonlinear nonautonomous differential equations. Adygeja, Maikop, 1993.

[22] Nehari Z.: Oscillation criteria for second-order linear differential equations. Trans. Amer. Math. Soc. 85 (1957), 428–445. | MR | Zbl

[23] Njoku F. I.: A note on the existence of infinitely many radially symmetric solutions of a quasilinear elliptic problem. Dyn. Cont. Discrete Impulsive Syst. 4 (1998), 227–239. | MR | Zbl

[24] Njoku F. I., Omari P., and Zanolin F.: Multiplicity of positive radial solutions of a quasilinear elliptic problem in a ball. (to appear), 1998. | MR

[25] Wang J.: On second order quasilinear oscillations. Funkcial. Ekvac. 41 (1998), 25–54. | MR | Zbl

[26] Wong J. S. W.: On second order nonlinear oscillation. Funkcial. Ekvac. 11 (1968), 207–234. | MR | Zbl

[27] Wong J. S. W.: On the generalized Emden-Fowler equation. SIAM Rev. 17 (1975), 339–360. | MR | Zbl