Ambarzumyan Type Theorems for a Class of Sturm-Liouville Problem
نویسندگان
چکیده
منابع مشابه
On a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations
Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.
متن کاملThe Asymptotic Form of Eigenvalues for a Class of Sturm-Liouville Problem with One Simple Turning Point
The purpose of this paper is to study the higher order asymptotic distributions of the eigenvalues associated with a class of Sturm-Liouville problem with equation of the form w??=(?2f(x)?R(x)) (1), on [a,b, where ? is a real parameter and f(x) is a real valued function in C2(a,b which has a single zero (so called turning point) at point 0x=x and R(x) is a continuously differentiable function. ...
متن کاملAsymptotic distributions of Neumann problem for Sturm-Liouville equation
In this paper we apply the Homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of Sturm-liouville type on $[0,pi]$ with Neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued Sign-indefinite number of $C^{1}[0,pi]$ and $lambda$ is a real parameter.
متن کاملExtremal Eigenvalues for a Sturm-Liouville Problem
We consider the fourth order boundary value problem (ry′′)′′+(py′)′+ qy = λwy, y(a) = y′(a) = y(b) = y′(b) = 0, which is used in a variety of physical models. For such models, the extremal values of the smallest eigenvalue help answer certain optimization problems, such as maximizing the fundamental frequency of a vibrating elastic system or finding the tallest column that will not buckle under...
متن کاملAmbarzumyan–type Theorems on Star Graphs
The so-called Ambarzumyan theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator − d2 dx2 +q with an integrable real-valued potential q on [0,π] are {n2 : n 0} , then q = 0 for almost all x ∈ [0,π] . In this work, the classical Ambarzumyan theorem is extended to star graphs with Dirac operators on its edges. We prove that if the spectrum of Dirac operator on star graphs ...
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: Cumhuriyet Science Journal
سال: 2017
ISSN: 2587-2680
DOI: 10.17776/csj.340393