The Eigenvalues of Three-Interval Sturm-Liouville Problems with Additional Impulsive Conditions
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Keywords:Sturm-Liouville Problems, Impulsive Conditions, Eigenvalue, Eigenfunction.
The main goal of this work is to study some properties of eigenvalues and corresponding eigenfunctions of a new type boundary value problems consisting of three-interval Sturm-Liouville equation The main goal of this work is to study some properties of eigenvalues and corresponding eigenfunctions of a new type boundary value problems consisting of three-interval Sturm-Liouville equation and additional impulsive conditions at the common endpoints.
The problem under consideration is reduced to classical periodic Sturm-Liouville problems, so the results obtained in this paper extend and generalize the corresponding classicals results. Note that the problem under consideration is not selfadjoint in the classical Hilbert space of square integrable functions. By using a new approaches we obtained some important properties of eigenvalues and eigenfunctions.
K. Aydemir and O. S. Mukhtarov, Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions, Advances in Difference Equations, 2016(1) 1-14, 2016.
M. Berzig and B.Samet, Positive solutions to periodic boundary value problems involving nonlinear operators of Meir-Keeler-type, Rendiconti del Circolo Matematico di Palermo, 61.2, 279-296, 2012.
P. Binding and H. Volkmer, A PrÄufer Angle Approach to the Periodic Sturm-Liouville Problem, The American Mathematical Monthly, Vol. 119, No. 6, pp. 477-484, 2012.
J. R. Cannon and G. H. Meyer, On a Difusion in a Fractured Medium, SIAM J. Appl. Math., 3 , pp. 434-448, 1971.
I. Çelik and G. Gokmen, Approximate solution of periodic Sturm-Liouville problems with Chebyshev collocation method. Applied mathematics and computa-tion 170.1, 285-295, 2005.
X. Haoa, L. Liu and Y. Wu, Existence and multiplicity results for nonlinear periodic boundary value problems, Nonlinear Analysis: Theory, Methods and Applications, 72.9-10: 3635-3642, 2010.
K. V., Khmelnytskaya, H. C. Rosu and A. Gonzlez. Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients, Annals of Physics, 325.3, 596-606, (2010).
H. Olğar, O. Sh. Mukhtarov and K. Aydemir, Some Properties of Eigenvalues and Generalized Eigenvectors of One Boundary Value Problem, Filomat, 3(3), 911-920, 2011.
H. Olğar and F. S. Muhtarov, The basis property of the system of weak eigenfunctions of a discontinuous Sturm-Liouville problem, Mediterranean Journal of Mathematics 14.3114, 2017.
H. Olğar, O. Sh. Mukhtarov and K. Aydemir, Operator-pencil realization of one Sturm-Liouville problem with transmission conditions, Applied and Computational Mathematics, 17.3, 284-294, 2018.
H. Pham Huy, E. Sanchez-Palencia, Phenom‘enes des transmission ‘a travers des couches minces de conductivite elevee J. Math. Anal. Appl., 47, 284-309, 1974.
E. Şen, Computation of eigenvalues and eigenfunctions of a Schrodinger-type boundary-value-transmission problem with retarded argument, Mathematical Methods in the Applied Sciences 41(16), 6604-6610, 2018.
Y. Zhao, C. Haibo, and Q. Bin, Periodic boundary value problems for second-order functional differential equations with impulse, Advances in Difference Equations 2014.1, 134, 2014.