Energy dependent potential problems for the one dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>p</mml:mi></mml:math>-Laplacian operator

Koyunbakan, Hikmet; Pinasco, Juan Pablo; Scarola, Cristian

doi:10.1016/j.nonrwa.2018.07.001

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…Hald [2][3][4]. Several works improved their methods and extended them to other problems and different boundary conditions [5][6][7][8][9][10], the quasilinear p-Laplacian operator [11,12], differential pencils [13,14], eigenvalue depending coefficients or boundary conditions [15,16], and also to quantum graphs [17][18][19][20][21][22][23]. However, most of these works assume the existence of a formula for the asymptotic behavior of eigenvalues or developed it using transmutation operators and Prufer's type transformations.…”

Section: Introductionmentioning

confidence: 99%

Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

Oviedo

Pinasco

2023

Math Methods in App Sciences

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In this work, we study the nodal inverse problem for Sturm–Liouville operators on quantum star graphs. We show that the zeros of eigenfunctions characterize the potential, and we present a simple algorithm that enables us to approximate it. The method does not rely on a priori information about the asymptotic behavior of eigenvalues. We manage to reduce the problem to a family of constant coefficient eigenvalue problems that can be solved explicitly and contain enough information to recover the potential. We also consider the multiplicity of eigenvalues and their vanishing properties, which only hold generically.

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Section: Introductionmentioning

confidence: 99%

Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

Oviedo

Pinasco

2023

Math Methods in App Sciences

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“…The solution of the inverse Sturm-Liouville problem has attracted many authors. This problem means finding the potential function by spectral data as spectrum, norming constants etc [1][2][3][4][5][6][7][8]. Inverse nodal problem means finding the potential function q by using zeros of eigenfunctions in literature [9,10].…”

Section: Introductionmentioning

confidence: 99%

Ambarzumyan theorem by zeros of eigenfunction

Kemaloglu

2023

International Journal of Mathematics and Computer in Engineering

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In this short paper, we give the proof of the Ambarzumyan theorem by zeros of eigenfunctions (nodal points) different from eigenvalues for the one-dimensional p-Laplacian eigenvalue problem. We show that the potential function q(x) is zero if the spectrum is in the specific form. We consider this theorem for p-Laplacian equation with periodic and anti-periodic cases. If p = 0, results are coincided with the results given for Sturm-Liouvile problem.

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“…12 Dual reciprocity hybrid radial boundary node method for Winkler and Pasternak foundation thin plate was researched by Yan et al 13 Vibration analysis of thin plates resting on Pasternak foundations was researched by Ehsan et al 14 using element free Galerkin method. Three approximate analytical solutions for thermal buckling of clamped thin rectangular functionally graded material plates resting on Pasternak elastic foundation were researched by Kiani et al 15 The performance of a rotated 5-point Laplacian operator for computing the harmonic potentials was investigated by Dahalan et al 16 Koyunbakan et al 17 analyzed a nonlinear eigenvalue problem for the p-Laplacian operator with zero Dirichlet boundary conditions. A metaheuristic optimization method for discretization of fractional Laplacian without discretization operator was studied by Mahata et al 18 Tan and Li 19 studied the solutions for nonlinear fractional differential equations with p-Laplacian operator nonlocal boundary value problem in a Banach space.…”

Section: Introductionmentioning

confidence: 99%

A computing method for bending problem of thin plate on Pasternak foundation

Gan

Yuan

et al. 2020

Advances in Mechanical Engineering

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The governing equation of the bending problem of simply supported thin plate on Pasternak foundation is degraded into two coupled lower order differential equations using the intermediate variable, which are a Helmholtz equation and a Laplace equation. A new solution of two-dimensional Helmholtz operator is proposed as shown in Appendix 1. The R-function and basic solutions of two-dimensional Helmholtz operator and Laplace operator are used to construct the corresponding quasi-Green function. The quasi-Green’s functions satisfy the homogeneous boundary conditions of the problem. The Helmholtz equation and Laplace equation are transformed into integral equations applying corresponding Green’s formula, the fundamental solution of the operator, and the boundary condition. A new boundary normalization equation is constructed to ensure the continuity of the integral kernels. The integral equations are discretized into the nonhomogeneous linear algebraic equations to proceed with numerical computing. Some numerical examples are given to verify the validity of the proposed method in calculating the problem with simple boundary conditions and polygonal boundary conditions. The required results are obtained through MATLAB programming. The convergence of the method is discussed. The comparison with the analytic solution shows a good agreement, and it demonstrates the feasibility and efficiency of the method in this article.

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Energy dependent potential problems for the one dimensionalp-Laplacian operator

Cited by 4 publications

References 33 publications

Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

Ambarzumyan theorem by zeros of eigenfunction

A computing method for bending problem of thin plate on Pasternak foundation

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