Geodesic
Estimation of operator norms in eigenvalue problems for equations with discontinuous operators
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 41-45 
D. K. Potapov. Estimation of operator norms in eigenvalue problems for equations with discontinuous operators. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 4, pp. 41-45. http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a5/
@article{ISU_2011_11_4_a5,
     author = {D. K. Potapov},
     title = {Estimation of operator norms in eigenvalue problems for equations with discontinuous operators},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {41--45},
     year = {2011},
     volume = {11},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a5/}
}
TY  - JOUR
AU  - D. K. Potapov
TI  - Estimation of operator norms in eigenvalue problems for equations with discontinuous operators
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2011
SP  - 41
EP  - 45
VL  - 11
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a5/
LA  - ru
ID  - ISU_2011_11_4_a5
ER  - 
%0 Journal Article
%A D. K. Potapov
%T Estimation of operator norms in eigenvalue problems for equations with discontinuous operators
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2011
%P 41-45
%V 11
%N 4
%U http://geodesic.mathdoc.fr/item/ISU_2011_11_4_a5/
%G ru
%F ISU_2011_11_4_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

Existence of solutions of problems with a spectral parameter for the equations with discontinuous operators is considered. The estimations of the operator norms for these problems are received. Dirichlet problem for the higher-order elliptic equation with discontinuous nonlinearity is considered as an appendix.

[1] Pavlenko V. N., Potapov D. K., “O suschestvovanii lucha sobstvennykh znachenii dlya uravnenii s razryvnymi operatorami”, Sib. mat. zhurn., 42:4 (2001), 911–919 | MR | Zbl

[2] Potapov D. K., “O suschestvovanii lucha sobstvennykh znachenii dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami v kriticheskom sluchae”, Vestn. S.-Peterb. un-ta. Ser. 10, 2004, no. 4, 125–132

[3] Potapov D. K., Zadachi so spektralnym parametrom i razryvnoi nelineinostyu, SPb., 2008, 99 pp.

[4] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, M., 1972, 416 pp. | MR

[5] Krasnoselskii M. A., Pokrovskii A. V., Sistemy s gisterezisom, M., 1983, 272 pp. | MR

[6] Potapov D. K., “O strukture mnozhestva sobstvennykh znachenii dlya uravnenii ellipticheskogo tipa vysokogo poryadka s razryvnymi nelineinostyami”, Differentsialnye uravneniya, 46:1 (2010), 150–152 | MR | Zbl

[7] Potapov D. K., “Otsenki differentsialnogo operatora v zadachakh so spektralnym parametrom dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, Vestn. Samarskogo gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2010, no. 5(21), 268–271 | DOI