Research Article
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Year 2022, Volume: 14 Issue: 2, 229 - 234, 30.12.2022
https://doi.org/10.47000/tjmcs.1012567

Abstract

References

  • Akbarfam, I., Jodayree, A., Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions, Mediterranean Journal Of Mathematics, 11(2)(2014), 447–462.
  • Allahverdiev, B.P., Bairamov, E., Ugurlu, E., Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, Journal of Mathematical Analysis and Applications, 401(1)(2013), 388–396.
  • Allahverdiev, B.P., Tuna, H., Titchmarsh-weyl theory for Dirac systems with transmission conditions, Mediterranean Journal of Mathematics, 15(4)(2018), 1–12.
  • Allahverdiev, B. P., Tuna, H., Eigenfunction Expansion for singular Sturm-Liouville problems with transmission conditions, Electronic Journal of Differential Equations, 3(2019), 4286–4302.
  • Aydemir, K., Mukhtarov, O.Sh., Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem, Boundary Value Problems, 2016(1)(2016), 1–16.
  • Aydemir, K., Olˇgar, H., Mukhtarov, O.Sh., Differential operator equations with interface conditions in modified direct sum spaces, Filomat, 32(3)(2018), 921–931.
  • Allegretto, W., Sturm theorems for degenerate elliptic equations, Proc. Am. Math. Soc., 129(2001), 3031–3035.
  • Dunninger, Dr., A Sturm comparison theorem for some degenerate quasilinear elliptic operators, Boll. Unione Mat. Ital., A7(9)(1995), 117–121.
  • Jaroˇs, J., Takaˆsi, K., Yoshida, N.,Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications, J. Inequal. Appl., (2006), 1–17.
  • Jaro, J., Kusano, T.,Second-order semilinear differential equations with external forcing terms, RIMS Kokyuroku, 984(1997), 191–197.
  • Jaro, J., Kusano, T., A Picone type identity for second order half-linear differential equations, Acta Math. Univ. Comen., 68(1999), 117–121.
  • Karlin, S., Lee, J.W., Periodic boundary-value problems and cyclic totally positive Green’s functions with applications to periodic spline theory, J. Differmtial Equations, 8(1970), 374–396.
  • Kreith, K, Oscillation Theory, Lecture Notes in Mathematics, vol. 324. Springer, Berlin, 1963.
  • Kreith, K., Picone’s identity and generalizations, Rend. Mat., 8(1975), 251–261.
  • Olˇgar, H., Mukhtarov, O.Sh., Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions, Journal of Mathematical Physics, 58(2017), 042201.
  • Mukhtarov, O.Sh., Olˇgar, H., Aydemir, K., Jabbarov, I.Sh., The operator-pencil realization of one Sturm-Liouville problem with transmission conditions, Applied and Computational Mathematics, 17(3)(2018), 284–294.
  • Pham Huy, H., Sanchez-Palencia, E., Ph´enom‘enes des transmission ‘a travers des couches minces de conductivit´e ´elev´ee, J. Math. Anal. Appl., 47(1974), 284–309.
  • Picone, M., Sui valori eccezionali di un parametro da cui dipende un’equazione differenziale lineare ordinaria del second’ordine, Ann. Scuola Norm. Sup. Pisa., 11(1909), 1–141.
  • Swanson, C.A., Comparison and Oscillation Theory of Linear Differential Equations, Vol. 48, Academic Prees, New York and London, 1968.
  • Sturm, C., Sur les ´equations diff´erentielles lin´eaires du second ordre, J. Math. Pures Appl., 1(1836), 106–186.
  • Şen, E., Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument, Mathematical Methods in the Applied Sciences, 41(2018), 6604–6610.
  • Şen, E., Spectral properties of boundary-value-transmission problems with a constant retarded argument, Turkish J Math., 43(2)(2019), 612–619.
  • Uğurlu, E., Bairamov, E., O Spectral analysis of eigenparameter dependent boundary value transmission problems, Journal Of Mathematical Analysis And Applications, 443(1)(2014), 482–494.
  • Yoshida, N, Oscillation criteria for half-linear partial differential equations via Picone’s identity, In: Proceedings of Equadiff, 11(2005), 589–598
  • Yoshida, N., Oscillation Theory of Partial Differential Equations, World Scientific, 2008.

Comparison Criteria for Three-Interval Sturm-Liouville Equations

Year 2022, Volume: 14 Issue: 2, 229 - 234, 30.12.2022
https://doi.org/10.47000/tjmcs.1012567

Abstract

This study devoted to the investigation of comparison properties for
periodic Sturm-Liouville problems, defined on three disjoint intervals together with
additional transfer conditions across the common endpoint of these intervals, so-called
transmission conditions. The results obtained generalize the corresponding
classical results of Sturm's comparison and oscillation theory.

References

  • Akbarfam, I., Jodayree, A., Resolvent operator and self-adjointness of Sturm-Liouville operators with a finite number of transmission conditions, Mediterranean Journal Of Mathematics, 11(2)(2014), 447–462.
  • Allahverdiev, B.P., Bairamov, E., Ugurlu, E., Eigenparameter dependent Sturm-Liouville problems in boundary conditions with transmission conditions, Journal of Mathematical Analysis and Applications, 401(1)(2013), 388–396.
  • Allahverdiev, B.P., Tuna, H., Titchmarsh-weyl theory for Dirac systems with transmission conditions, Mediterranean Journal of Mathematics, 15(4)(2018), 1–12.
  • Allahverdiev, B. P., Tuna, H., Eigenfunction Expansion for singular Sturm-Liouville problems with transmission conditions, Electronic Journal of Differential Equations, 3(2019), 4286–4302.
  • Aydemir, K., Mukhtarov, O.Sh., Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem, Boundary Value Problems, 2016(1)(2016), 1–16.
  • Aydemir, K., Olˇgar, H., Mukhtarov, O.Sh., Differential operator equations with interface conditions in modified direct sum spaces, Filomat, 32(3)(2018), 921–931.
  • Allegretto, W., Sturm theorems for degenerate elliptic equations, Proc. Am. Math. Soc., 129(2001), 3031–3035.
  • Dunninger, Dr., A Sturm comparison theorem for some degenerate quasilinear elliptic operators, Boll. Unione Mat. Ital., A7(9)(1995), 117–121.
  • Jaroˇs, J., Takaˆsi, K., Yoshida, N.,Picone-type inequalities for nonlinear elliptic equations with first-order terms and their applications, J. Inequal. Appl., (2006), 1–17.
  • Jaro, J., Kusano, T.,Second-order semilinear differential equations with external forcing terms, RIMS Kokyuroku, 984(1997), 191–197.
  • Jaro, J., Kusano, T., A Picone type identity for second order half-linear differential equations, Acta Math. Univ. Comen., 68(1999), 117–121.
  • Karlin, S., Lee, J.W., Periodic boundary-value problems and cyclic totally positive Green’s functions with applications to periodic spline theory, J. Differmtial Equations, 8(1970), 374–396.
  • Kreith, K, Oscillation Theory, Lecture Notes in Mathematics, vol. 324. Springer, Berlin, 1963.
  • Kreith, K., Picone’s identity and generalizations, Rend. Mat., 8(1975), 251–261.
  • Olˇgar, H., Mukhtarov, O.Sh., Weak eigenfunctions of two-interval Sturm-Liouville problems together with interaction conditions, Journal of Mathematical Physics, 58(2017), 042201.
  • Mukhtarov, O.Sh., Olˇgar, H., Aydemir, K., Jabbarov, I.Sh., The operator-pencil realization of one Sturm-Liouville problem with transmission conditions, Applied and Computational Mathematics, 17(3)(2018), 284–294.
  • Pham Huy, H., Sanchez-Palencia, E., Ph´enom‘enes des transmission ‘a travers des couches minces de conductivit´e ´elev´ee, J. Math. Anal. Appl., 47(1974), 284–309.
  • Picone, M., Sui valori eccezionali di un parametro da cui dipende un’equazione differenziale lineare ordinaria del second’ordine, Ann. Scuola Norm. Sup. Pisa., 11(1909), 1–141.
  • Swanson, C.A., Comparison and Oscillation Theory of Linear Differential Equations, Vol. 48, Academic Prees, New York and London, 1968.
  • Sturm, C., Sur les ´equations diff´erentielles lin´eaires du second ordre, J. Math. Pures Appl., 1(1836), 106–186.
  • Şen, E., Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument, Mathematical Methods in the Applied Sciences, 41(2018), 6604–6610.
  • Şen, E., Spectral properties of boundary-value-transmission problems with a constant retarded argument, Turkish J Math., 43(2)(2019), 612–619.
  • Uğurlu, E., Bairamov, E., O Spectral analysis of eigenparameter dependent boundary value transmission problems, Journal Of Mathematical Analysis And Applications, 443(1)(2014), 482–494.
  • Yoshida, N, Oscillation criteria for half-linear partial differential equations via Picone’s identity, In: Proceedings of Equadiff, 11(2005), 589–598
  • Yoshida, N., Oscillation Theory of Partial Differential Equations, World Scientific, 2008.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Oktay Mukhtarov 0000-0001-7480-6857

Kadriye Aydemir 0000-0002-8378-3949

Early Pub Date December 23, 2022
Publication Date December 30, 2022
Published in Issue Year 2022 Volume: 14 Issue: 2

Cite

APA Mukhtarov, O., & Aydemir, K. (2022). Comparison Criteria for Three-Interval Sturm-Liouville Equations. Turkish Journal of Mathematics and Computer Science, 14(2), 229-234. https://doi.org/10.47000/tjmcs.1012567
AMA Mukhtarov O, Aydemir K. Comparison Criteria for Three-Interval Sturm-Liouville Equations. TJMCS. December 2022;14(2):229-234. doi:10.47000/tjmcs.1012567
Chicago Mukhtarov, Oktay, and Kadriye Aydemir. “Comparison Criteria for Three-Interval Sturm-Liouville Equations”. Turkish Journal of Mathematics and Computer Science 14, no. 2 (December 2022): 229-34. https://doi.org/10.47000/tjmcs.1012567.
EndNote Mukhtarov O, Aydemir K (December 1, 2022) Comparison Criteria for Three-Interval Sturm-Liouville Equations. Turkish Journal of Mathematics and Computer Science 14 2 229–234.
IEEE O. Mukhtarov and K. Aydemir, “Comparison Criteria for Three-Interval Sturm-Liouville Equations”, TJMCS, vol. 14, no. 2, pp. 229–234, 2022, doi: 10.47000/tjmcs.1012567.
ISNAD Mukhtarov, Oktay - Aydemir, Kadriye. “Comparison Criteria for Three-Interval Sturm-Liouville Equations”. Turkish Journal of Mathematics and Computer Science 14/2 (December 2022), 229-234. https://doi.org/10.47000/tjmcs.1012567.
JAMA Mukhtarov O, Aydemir K. Comparison Criteria for Three-Interval Sturm-Liouville Equations. TJMCS. 2022;14:229–234.
MLA Mukhtarov, Oktay and Kadriye Aydemir. “Comparison Criteria for Three-Interval Sturm-Liouville Equations”. Turkish Journal of Mathematics and Computer Science, vol. 14, no. 2, 2022, pp. 229-34, doi:10.47000/tjmcs.1012567.
Vancouver Mukhtarov O, Aydemir K. Comparison Criteria for Three-Interval Sturm-Liouville Equations. TJMCS. 2022;14(2):229-34.