Yıl 2022,
Cilt: 14 Sayı: 2, 229 - 234, 30.12.2022
Oktay Mukhtarov
,
Kadriye Aydemir
Kaynakça
- 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
Yıl 2022,
Cilt: 14 Sayı: 2, 229 - 234, 30.12.2022
Oktay Mukhtarov
,
Kadriye Aydemir
Öz
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.
Kaynakça
- 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.