Eigenfunction Expansions for a Sturm–Liouville Problem on Time Scales
نویسنده
چکیده
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.
منابع مشابه
Eigenfunction expansion in the singular case for q-Sturm-Liouville operators
In this work, we prove the existence of a spectral function for singular q-Sturm-Liouville operator. Further, we establish a Parseval equality and expansion formula in eigenfunctions by terms of the spectral function.
متن کاملSturm-Liouville Fuzzy Problem with Fuzzy Eigenvalue Parameter
This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.
متن کاملEigenfunction expansions in L2 spaces for boundary value problems on time-scales
Let T⊂ R be a bounded time-scale, with a = inf T, b = supT. We consider the weighted, linear, eigenvalue problem −(pu ) (t)+ q(t)u (t)= λw(t)u (t), t ∈ Tκ , c00u(a)+ c01u (a)= 0, c10u ( ρ(b) )+ c11u (ρ(b))= 0, for suitable functions p, q and w and λ ∈ R. Problems of this type on time-scales have normally been considered in a setting involving Banach spaces of continuous functions on T. In this ...
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 کاملInverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...
متن کامل