Browsing by Author "Turhan KÖPRÜBAŞI"

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A Study of Impulsive Discrete Dirac System With Hyperbolic Eigenparameter
(2021-01-21) KÖPRÜBAŞI T.; Turhan KÖPRÜBAŞI; Koprubasi, T
Let L denote the discrete Dirac operator generated in ℓ2 (N,C2) by the difference operators of first order with boundary and impulsive conditions where {pn} n∈N, {qn} n∈N are real sequences, λ = 2 sinh is a hyperbolic eigenparameter and △ is forward operator. In this paper, the spectral properties of L such as the spectrum, the eigenvalues, the scattering function and their properties are given with an example in the special cases under the condition
A study of impulsive discrete Dirac system with hyperbolic eigenparameter
(2021-01-01) Turhan KÖPRÜBAŞI
Let L denote the discrete Dirac operator generated in ℓ2 ( N, C 2 ) by the difference operators of first order { △y (2) n + pny (1) n = λy(1) n △y (1) n−1 + qny (2) n = λy(2) n , n ∈ N {k − 1, k, k + 1} with boundary and impulsive conditions y (1) 0 = 0 , ( y (1) k+1 y (2) k+2 ) = θ ( y (2) k−1 y (1) k−2 ) ; θ = ( θ1 θ2 θ3 θ4 ) , {θi}i=1,2,3,4 ∈ R where {pn}n∈N , {qn}n∈N are real sequences, λ = 2 sinh ( z 2 ) is a hyperbolic eigenparameter and △ is forward operator. In this paper, the spectral properties of L such as the spectrum, the eigenvalues, the scattering function and their properties are given with an example in the special cases under the condition ∑∞ n=1 n (|pn| + |qn|) < ∞.
Discrete impulsive Sturm–Liouville equation with hyperbolic eigenparameter
(2022-05-01) Yelda AYGAR KÜÇÜKEVCİLİOĞLU; Turhan KÖPRÜBAŞI
Let L denote the selfadjoint difference operator of second order with boundary and impulsive conditions generated in ℓ2 (N) by an−1yn−1 + bnyn + anyn+1 = (2 cosh z) yn , n ∈ N {k − 1, k, k + 1} , y0 = 0 , { yk+1 = θ1yk−1 △yk+1 = θ2 ▽ yk−1 , θ1, θ2 ∈ R, where {an}n∈N , {bn}n∈N are real sequences and △, ▽ are respectively forward and backward operators. In this paper, the spectral properties of L such as the resolvent operator, the spectrum, the eigenvalues, the scattering function and their properties are investigated. Moreover, an example about the scattering function and the existence of eigenvalues is given in the special cases, if ∑∞ n=1 n (|1 − an| + |bn|) < ∞.
Oscillation criteria for higher-order neutral type difference equations
(2020-09-01) Zafer ÜNAL; Yaşar BOLAT; Turhan KÖPRÜBAŞI
In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form ∆(rn(∆k−1 (yn + pnyτn )) + qnf(yσn ) = 0, n ≥ n0, (0.1) where rn, pn, qn ∈ [n0, ∞), rn > 0, qn > 0; 0 ≤ pn ≤ p0 < ∞; limn→∞ τn = ∞, limn→∞ σn = ∞; σn ≤ n, σn is nondecreasing; ∆τn ≥ τ0 > 0; τσ = στ ;f(u) u ≥ m > 0 for u ̸= 0. Moreover, we provide some examples to illustrate our main results.
THE CUBIC EIGENPARAMETER DEPENDENT DISCRETE DIRAC EQUATIONS WITH PRINCIPAL FUNCTIONS
(2019-12-01) Turhan KÖPRÜBAŞI
Let us consider the Boundary Value Problem (BVP) for the discrete Dirac Equations ( an+1y (2) n+1 + bny (2) n + pny (1) n = y(1) n an1y (1) n1 + bny (1) n + qny (2) n = y(2) n ; n 2 N; (0.1) (0 + 1 + 2 2 + 3 3 )y (2) 1 + (0 + 1 + 2 2 + 3 3 )y (1) 0 = 0; (0.2) where (an); (bn); (pn) and (qn); n 2 N are complex sequences, i ; i 2 C; i = 0; 1; 2 and is a eigenparameter. Discussing the eigenvalues and the spectral singularities, we prove that the BVP (0.1), (0.2) has a Önite number of eigenvalues and spectral singularities with a Önite multiplicities, if X1 n=1 exp("n ) (j1 anj + j1 + bnj + jpnj + jqnj) < 1; holds, for some " > 0 and 1 2.
THE CUBIC EIGENPARAMETER DEPENDENT DISCRETE DIRAC EQUATIONS WITH PRINCIPAL FUNCTIONS
(2019.01.01) Koprubasi, T; Turhan KÖPRÜBAŞI
Let us consider the Boundary Value Problem (BVP) for the discrete Dirac Equations ( an+1y (2) n+1 + bny (2) n + pny (1) n = y(1) n an1y (1) n1 + bny (1) n + qny (2) n = y(2) n ; n 2 N; (0.1) (0 + 1 + 2 2 + 3 3 )y (2) 1 + (0 + 1 + 2 2 + 3 3 )y (1) 0 = 0; (0.2) where (an); (bn); (pn) and (qn); n 2 N are complex sequences, i ; i 2 C; i = 0; 1; 2 and is a eigenparameter. Discussing the eigenvalues and the spectral singularities, we prove that the BVP (0.1), (0.2) has a Önite number of eigenvalues and spectral singularities with a Önite multiplicities, if X1 n=1 exp("n ) (j1 anj + j1 + bnj + jpnj + jqnj) < 1; holds, for some " > 0 and 1 2.
Uniqueness of the solution to the inverse problem of scattering theory for spectral parameter dependent Klein-Gordon s-wave equation
(2023-03-30) Esra KIR ARPAT; Turhan KÖPRÜBAŞI
In the present work, the inverse problem of the scattering theory for Klein-Gordon s-wave equation with a spectral parameter in the boundary condition is investigated. We define the scattering data set, and obtain the main equation of operator. Furthermore, the uniqueness of the solution of the inverse problem is proved.