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.
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
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.
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.
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.
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.