Multiplicity results for a generalized Sturm-Liouville dynamical system on time scales
نویسندگان
چکیده
منابع مشابه
Sturm–liouville Operators on Time Scales
We establish the connection between Sturm–Liouville equations on time scales and Sturm–Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm–Liouville equations on time scales which have been obtained by various authors in the past.
متن کاملEigenfunction Expansions for a Sturm–Liouville Problem on Time Scales
In this paper we investigate a Sturm–Liouville eigenvalue problem on time scales. Existence of the eigenvalues and eigenfunctions is proved. Mean square convergent and uniformly convergent expansions in the eigenfunctions are established. AMS subject classification: 34L10.
متن کاملMultiplicity of Sturm-liouville Eigenvalues
The geometric multiplicity of each eigenvalue of a self-adjoint Sturm-Liouville problem is equal to its algebraic multiplicity. This is true for regular problems and for singular problems with limit-circle endpoints, including the case when the leading coefficient changes sign.
متن کاملAn Expansion Theorem for a Sturm–Liouville Operator on Semi-Unbounded Time Scales
In this study, we establish a Parseval equality and an expansion formula for a Sturm– Liouville operator on semi-unbounded time scales. AMS subject classification: 34L10.
متن کاملExistence and Multiplicity Results for a Mixed Sturm-liouville Type Boundary Value Problem
where the potentials are given functions. Under various boundary conditions, Sturm and Liouville established that solutions of problem (1) can exist only for particular values of the real parameter λ, which is called an eigenvalue. Relevant examples of linear Sturm-Liouville problems are the Bessel equation and the Legendre equation. The classical Sturm-Liouville theory does not depend upon the...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2011
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2011-24