Conjugacy and disconjugacy criteria for second order linear ordinary differential equations
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 313-323 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 34C10
Keywords: second order equation; conjugacy criteria; disconjugacy criteria
@article{ARM_2000_36_4_a8,
     author = {Chantladze, T. and Lomtatidze, A. and Ugulava, D.},
     title = {Conjugacy and disconjugacy criteria for second order linear ordinary differential equations},
     journal = {Archivum mathematicum},
     pages = {313--323},
     year = {2000},
     volume = {36},
     number = {4},
     mrnumber = {1811176},
     zbl = {1054.34053},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a8/}
}
TY  - JOUR
AU  - Chantladze, T.
AU  - Lomtatidze, A.
AU  - Ugulava, D.
TI  - Conjugacy and disconjugacy criteria for second order linear ordinary differential equations
JO  - Archivum mathematicum
PY  - 2000
SP  - 313
EP  - 323
VL  - 36
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a8/
LA  - en
ID  - ARM_2000_36_4_a8
ER  - 
%0 Journal Article
%A Chantladze, T.
%A Lomtatidze, A.
%A Ugulava, D.
%T Conjugacy and disconjugacy criteria for second order linear ordinary differential equations
%J Archivum mathematicum
%D 2000
%P 313-323
%V 36
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a8/
%G en
%F ARM_2000_36_4_a8
Chantladze, T.; Lomtatidze, A.; Ugulava, D. Conjugacy and disconjugacy criteria for second order linear ordinary differential equations. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 313-323. http://geodesic.mathdoc.fr/item/ARM_2000_36_4_a8/

[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

[2] Chanturia T. A.: On conjugacy of high order ordinary differential equations. Georgian Math. J., vol. 1 (1994), No. 1, 1–8. | MR

[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

[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

[5] Došlý O.: The multiplicity criteria for zero points of second order differential equations. Math. Slovaca, vol. 42 (1992), No. 2, 181–193. | MR

[6] Došlý O.: Conjugacy criteria for second order differential equations. Rocky Mountain J. of Math., vol. 23 (1993), No. 3, 849–861. | MR

[7] Hartman P.: Ordinary differential equations. John Wiley & Sons, Inc., New–York–London–Sydney, 1964. | MR | Zbl

[8] Hawking S. W., Penrose R.: The singularities of gravitational collapse and cosmology. Proc. Roy. Soc. London, Ser. A, vol. 314 (1970), 529–548. | MR | Zbl

[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

[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

[11] Müller–Pfeiffer E.: Nodal domains of one–or–two–dimensional elliptic differential equations. Z. Anal. Anwendungen, vol. 7 (1988), 135–139. | MR

[12] Peña S.: Conjugacy criteria for half–linear differential equations. Arch. Math., vol. 35 (1999), No. 1, 1–11. | MR

[13] Tipler F. J.: General relativity and ordinary differential equations. J. Differential Equations, vol. 30 (1978), 165–174. | MR

[14] Willet D.: On the oscillatory behaviour of the solutions of second order linear differential equations. Ann. Polon. Math., vol. 21 (1969), 175–194.