×

A remark on conjugacy of half-linear second order differential equations. (English) Zbl 0959.34025

Sufficient conditions for the existence of a nontrivial solution to a half-linear second-order differential equation, having at least two different zeros in a given interval, are derived.

MSC:

34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] BORŮVKA O.: Lineare Differentialtransformationen 2. Ordnung. Deutscher Veilag der Wissenschaften, Berlin, 1991.
[2] DOŠLÝ O.: Multiplicity criteria for zero points of second order differential equations. Math. Slovaca 42 (1992), 181-193. · Zbl 0754.34026
[3] DOŠLÝ O.: Conjugacy criteria for second order differential equations. Rocky Mountain J. Math. 23 (1993), 849-891. · Zbl 0794.34025 · doi:10.1216/rmjm/1181072527
[4] DOŠLÝ O.: Existence of conjugate points for linear differential systems. Math. Slovaca 40 (1990), 87-99. · Zbl 0744.34013
[5] DOŠLÝ O.: Oscillation criteria for half-linear differential equations. Hiroshima J. Math. 28 (1998), 507-521. · Zbl 0920.34042
[6] DOŠLÝ O.-ELBERT Á.: Conjugacy criteria for half-linear second order differential equations. Proc. Roy Soc. Edinburgh Sect. A (2000)
[7] ELBERT Á.: A half-linear second order differential equation. Theory of Differential Equation. Colloq. Math. Soc. Janos Bolyai 30, North-Holland, Amsterdam, 1979, pp. 158-180.
[8] ELBERT Á.: Oscillation and nonosdilation theorems for some non-linear ordinary differential equations. Lecture Notes in Math. 964, Springer, New York, 1982, pp. 187-212.
[9] ELBERT Á.: On the half-linear second order differential equations. Acta Math. Hungar. 49 (1987), 487-508. · Zbl 0656.34008 · doi:10.1007/BF01951012
[10] ELBERT Á.-KUSANO T.: Principal solutions of nonoscillatory half-linear differential equations. Adv. Math. Sci. Appl. 18 (1998), 745-759. · Zbl 0914.34031
[11] ELBERT Á.-KUSANO T.-TANIGAWA T.: An oscillatory half-linear differential equation. Arch. Math. (Basel) 33 (1997), 355-361. · Zbl 0914.34026
[12] JAROŠ J.-KUSANO T.: Picone’s identity for half-linear second order differential equations. Acta Math. Univ. Comenian. 68 (1999), 137-151. · Zbl 0926.34023
[13] LI H. J.: Oscillation criteria for half-linear second order differential equations. Hirosima Math. J. 25 (1995), 571-583. · Zbl 0872.34018
[14] LI H. J.-YEH C. C.: Sturmian comparison theorem for half-linear second order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 125 (1996), 1193-1204. · Zbl 0873.34020 · doi:10.1017/S0308210500030468
[15] MÜLLER-PFEIFFER E.: Existence of conjugate points for second and fourth order differential equations. Proc. Roy Soc. Edinburgh Sect. A 89 (1981), 281-291. · Zbl 0481.34019 · doi:10.1017/S0308210500020291
[16] MÜLLER-PFEIFFER E.: Nodal domains of one- or two-dimensional elliptic differential equations. Z. Anal. Anwendungen 7 (1988), 135-139. · Zbl 0657.35042
[17] PEŇA S.: Conjugacy criteria for half-linear differential equations. Arch. Math. (Brno) 35 (1999), 1-11. · Zbl 1054.34055
[18] SCHMINKE U. W.: The lower spectrum of Schrödinger operators. Arch. Rational Mech. Anal. 75 (1981), 147-155. · Zbl 0455.35046
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.