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# Article

 Title: Conjugacy and disconjugacy criteria for second order linear ordinary differential equations (English) Author: Chantladze, T. Author: Lomtatidze, A. Author: Ugulava, D. Language: English Journal: Archivum Mathematicum ISSN: 0044-8753 (print) ISSN: 1212-5059 (online) Volume: 36 Issue: 4 Year: 2000 Pages: 313-323 Summary lang: English . Category: math . Summary: Conjugacy and disconjugacy criteria are established for the equation $u^{\prime \prime }+p(t)u=0\,,$ where $p:]-\infty ,+\infty [\rightarrow ]-\infty ,+\infty [$ is a locally summable function. (English) Keyword: second order equation Keyword: conjugacy criteria Keyword: disconjugacy criteria MSC: 34C10 idZBL: Zbl 1054.34053 idMR: MR1811176 . Date available: 2008-06-06T22:26:28Z Last updated: 2012-05-10 Stable URL: http://hdl.handle.net/10338.dmlcz/107746 . Reference: [1] Ahlbrandt C. D., Hinton D. B., Lewis R. T.: The effect of variable change on oscillation and disconjugacy criteria with applications to spectral and asymptotic theory.J. Math. Anal. Appl., vol. 81 (1981), pp. 234–277. MR 0618771 Reference: [2] Chanturia T. A.: On conjugacy of high order ordinary differential equations.Georgian Math. J., vol. 1 (1994), No. 1, 1–8. MR 1251490 Reference: [3] Chantladze T., Kandelaki N., Lomtatidze A.: On zeros of solutions of the second order singular half–linear equation.Mem. Differential Equations Math. Phys., vol. 17 (1999), 127–154. MR 1710580 Reference: [4] Chantladze T., Kandelaki N., Lomtatidze A.: Oscillation and nonoscillation criteria for the second order linear equation.Georgian Math. J., vol. 6 (1999), No. 5, 401–414. MR 1692963 Reference: [5] Došlý O.: The multiplicity criteria for zero points of second order differential equations.Math. Slovaca, vol. 42 (1992), No. 2, 181–193. MR 1170102 Reference: [6] Došlý O.: Conjugacy criteria for second order differential equations.Rocky Mountain J. of Math., vol. 23 (1993), No. 3, 849–861. MR 1245450 Reference: [7] Hartman P.: Ordinary differential equations.John Wiley & Sons, Inc., New–York–London–Sydney, 1964. Zbl 0125.32102, MR 0171038 Reference: [8] Hawking S. W., Penrose R.: The singularities of gravitational collapse and cosmology.Proc. Roy. Soc. London, Ser. A, vol. 314 (1970), 529–548. Zbl 0954.83012, MR 0264959 Reference: [9] Mingarelli A. B.: On the existence of conjugate points for the second order ordinary differential equation.SIAM J. Math. Anal., vol. 17 (1986), No. 1, 1–6. MR 0819206 Reference: [10] Müller–Pfeiffer E.: Existence of conjugate points for second and fourth order differential equations.Proc. Roy. Soc. Edinburgh, Sect. A, vol. 89 (1981), 281–291. MR 0635764 Reference: [11] Müller–Pfeiffer E.: Nodal domains of one–or–two–dimensional elliptic differential equations.Z. Anal. Anwendungen, vol. 7 (1988), 135–139. MR 0951346 Reference: [12] Peña S.: Conjugacy criteria for half–linear differential equations.Arch. Math., vol. 35 (1999), No. 1, 1–11. MR 1684518 Reference: [13] Tipler F. J.: General relativity and ordinary differential equations.J. Differential Equations, vol. 30 (1978), 165–174. MR 0513268 Reference: [14] Willet D.: On the oscillatory behaviour of the solutions of second order linear differential equations.Ann. Polon. Math., vol. 21 (1969), 175–194. .

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