Asymptotics of Eigenvalues for Sturm-Liouville Problem with Eigenvalue in the Boundary Condition for Differentiable Potential

Sturm-Liouville equation on a finite interval together with boundary conditions arises from the infinitesimal, vertical vibrations of a string with the ends subject to various constraints. The coefficient (also called potential) function in the differential equation is in a close relationship with the density of the string. In this sense, the computation of solutions plays a rather important role in both mathematical and physical fields. In this study, asymptotic behaviors of the solutions for Sturm-Liouville problems associated with polynomially eigenparameter dependent boundary conditions are obtained when the potential function is real valued 𝑳𝟏- function on the interval (𝟎, 𝟏). Besides, the asymptotic formulae are given for the derivatives of the solutions.

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Asymptotics of Eigenvalues for Sturm-Liouville Problem with Eigenvalue in the Boundary Condition for Differentiable Potential

Abstract: Abstract. In this paper, we obtain asymptotic estimates of eigenvalues for regular SturmLiouville problems having the eigenvalue parameter in the boundary condition with the potential that is continuous, also its differentiation exists and is integrable.

Cited by 2 publications

References 12 publications

Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

Asymptotic Behavior for Eigenvalues of the Singular Sturm-Liouville Problem with Transmission Conditions

Sturm-Liouville Problems with Polynomially Eigenparameter Dependent Boundary Conditions

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