On the Spectral Properties of A Sturm-Liouville Problem with Eigenparameter in the Boundary Condition
نویسندگان
چکیده
منابع مشابه
Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions
In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining a new Hilbert space and using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...
متن کاملsome spectral properties of sturm-liouville problem with transmission conditions
we investigate the boundary-value problem generated by the sturm-liouville equation withdiscontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditionsat the point of discontinuity. with a different approach we introduce an adequate hilbert spaceformulation, investigate some properties of eigenvalues, green’s function and resolvent operator, andfind simple c...
متن کاملNon-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter
and Applied Analysis 3 2. Jost Solution of 1.4 We will denote the solution of 1.4 satisfying the condition lim x→∞ y x, λ e−iλx 1, λ ∈ C : {λ : λ ∈ C, Imλ ≥ 0}, 2.1 by e x, λ . The solution e x, λ is called the Jost solution of 1.4 . Under the condition ∫∞ 0 x ∣ ∣q x ∣ ∣dx < ∞, 2.2 the Jost solution has a representation
متن کاملEigenparameter Dependent Inverse Sturm-Liouville Problems
Uniqueness of and numerical techniques for the inverse Sturm-Liouville problem with eigenparameter dependent boundary conditions will be discussed. We will use a Gel’fand-Levitan technique to show that the potential q in u00 þ qu 1⁄4 u, 0 < x < 1 uð0Þ 1⁄4 0, ða þ bÞuð1Þ 1⁄4 ðc þ d Þu0ð1Þ can be uniquely determined using spectral data. In the presence of finite spectral data, q can be reconstruc...
متن کاملEigenparameter Dependent Inverse Sturm-Liouville Problems
The author studies the inverse scattering problem for a boundary value problem of a generalized one dimensional Schrödinger type with a discontinuous coefficient and eigenparameter dependent boundary condition. The solutions of the considered eigenvalue equation is presented and its scattering function that satisfies some properties is induced. The discrete spectrum is studied and the resolvent...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2019
ISSN: 2651-477X
DOI: 10.15672/hujms.479445