The spectral analysis of some not self-adjoint operator pencil with a discontinuous coefficient

1Orudzhev, HD
2Efendiev, RF
1Qafqaz University, Baku, Azerbaijan
2Baku State University, Azerbaijan
Dopov. Nac. akad. nauk Ukr. 2014, 4:25-31
https://doi.org/10.15407/dopovidi2014.04.025
Section: Mathematics
Language: Russian
Abstract: 

The direct and inverse problems for the Schrödinger equation on the whole axis with complex periodic potentials and discontinuous right-hand side are investigated. The main properties of the fundamental solutions and the spectrum of the problem are studied. The inverse problem is formulated, and a constructive procedure for its solution is given.

Keywords: not self-adjoint operator pencil, spectral analysis
References: 

1. Makris K. G., El-Ganainy R., Christodoulides D. N., Musslimani Z. H. Phys. Rev. A, 2010, 81, No. 6: 063807. https://doi.org/10.1103/PhysRevA.81.063807
2. Makris K. G., El-Ganainy R., Christodoulides D. N., Musslimani Z. H. Phys. Rev. Lett., 2008, 100, No. 10: 103904. https://doi.org/10.1103/PhysRevLett.100.103904
3. Grinbereg N. I. Mat. sb., 1990, 181, No. 8: 1114–1129 (in Russian).
4. Gasymov M. G. Funkts. analiz i ego prilozheniia, 1980, 14, No. 1: 14–19 (in Russian).
5. Gorbachuk V. I., Gorbachuk M. L. Boundary value problems for differential-operator equations. Kyiv: Nauk. dumka, 1984 (in Russian).
6. Efendiev R. F. Appl. Anal., 2011, 90, No. 12: 1837–1849. https://doi.org/10.1080/00036811.2010.532491
7. Efendiev R. F., Orudzhev H. D. J. Math. Physics, Analysis, Geometry, 2010, 6, No. 3: 255–265.
8. Efendiev R. F. Theoret. and Math. Physics., 2005, 145, No. 1: 1457–1461. https://doi.org/10.1007/s11232-005-0171-1