Uniqueness of the solution of half inverse problem for the impulsive Sturm Liouville operator
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
The half-inverse spectral problem for an impulsive Sturm--Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm--Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on $\left( 0,\frac{\pi }{2}\right) $, then only one spectrum is sufficient to determine $q(x)$ on the interval $\left( 0,\pi \right) $ for this problem
Abstract
The half-inverse spectral problem for an impulsive Sturm--Liouville operator consists in reconstruction of this operator from its spectrum and half of the potential. In this study, the spectrum of the impulsive Sturm--Liouville problem is given and by using the Hochstadt and Lieberman's method we show that if $q(x)$ is prescribed on $\left( 0,\frac{\pi }{2}\right) $, then only one spectrum is sufficient to determine $q(x)$ on the interval $\left( 0,\pi \right) $ for this problem
참고문헌 (15)
- P. E. Bulavin, "Solution of the nonhomogeneous heat conduction equation for multilayered bodies", Int. Chem. Engng, 5, pp.112~115 (1965)
- G. Freiling, "Inverse Sturm-Liouville Problems and Their Applications" (2001), Nova Science
- I. M. Gelfand, "On the determination of a differential equation from its spectral function", Amer. Math. Transl, 1(2), pp.239~253 (1951)
- F. Gesztesy, "Inverse spectral analysis with partial information on the potential II: The case of discrete spectrum", Trans. Amer. Math. Soc, 352(6), pp.2765~2787 (2000)
- O. H. Hald, "Discontinuous inverse eigenvalue problem", Comm. Pure Appl. Math, 37(5), pp.539~577 (1984)
- H. Hochstadt, "An inverse Sturm-Liouville problem with mixed given data", SIAM J. Appl. Math, 34(4), pp.676~680 (1978)
- O. R. Hryniv, "Half-inverse spectral problems for Sturm–Liouville operators with singular potentials", Inverse Problems, 20(5), pp.1423~1444 (2004)
- B. M. Levitan, "Sturm-Liouville and Dirac Operators" (1991), Kluwer Academic Publishers
- M. M. Malamud, "Questions of uniqueness in inverse problems for systems of differential equations on a finite interval", Tr. Mosk. Mat. Obs, 60, pp.199~258 (1999)
- V. A. Marchenko, "Sturm-Liouville Operators and Their Applications" (1986), Birkhauser
- M. N. Ozisik, "Boundary Value Problems of Heat Conduction" (1989), Dower
- L. Sakhnovich, "Half inverse problems on the finite interval", Inverse Problems, 17(3), pp.527~532 (2001)
- C.-F. Yang, "A half-inverse problem with eigenparameter dependent boundary conditions", Numer. Funct. Anal. Optim, 31(6), pp.754~762 (2010)
- C.-F. Yang, "Hochstadt-Lieberman theorem for Dirac operator with eigenparameter de- pendent boundary conditions", Nonlinear Anal, 74(7), pp.2475~2484 (2011)
- V. F. Zdanovic, "Formulae for the zeros of Dirichlet polynomials and quasi- polynomials", Dokl. Acad. Nauk SSSR, 135(8), pp.1046~1049 (1960)