Geodesic
Estimation of the bifurcation parameter in spectral problems for equations with discontinuous operators
Ufa mathematical journal, Tome 3 (2011) no. 1, pp. 42-44
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We consider the existence of solutions of the eigenvalue problem for nonlinear equations with discontinuous operators in the reflexive Banach space. Coercivity of the corresponding mapping is not supposed. An upper bound for the value of the bifurcation parameter is obtained by the variational method. This result confirms that the upper bound for the value of the bifurcation parameter obtained earlier in spectral problems for elliptic equations with discontinuous nonlinearities is true.
Keywords: eigenvalues, spectral problems, discontinuous operator, variational method, upper bound, bifurcation parameter. 
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D. K. Potapov. Estimation of the bifurcation parameter in spectral problems for equations with discontinuous operators. Ufa mathematical journal, Tome 3 (2011) no. 1, pp. 42-44. http://geodesic.mathdoc.fr/item/UFA_2011_3_1_a3/

[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] Goldshtik M. A., “Matematicheskaya model otryvnykh techenii neszhimaemoi zhidkosti”, Dokl. AN SSSR, 147:6 (1962), 1310–1313

[4] L. E. Fraenkel, M. S. Berger, “A global theory of steady vortex rings in an ideal fluid”, Acta Math., 132:1 (1974), 13–51 | DOI | MR | Zbl

[5] H. J. Kuiper, “On positive solutions of nonlinear elliptic eigenvalue problems”, Rend. Circ. Mat. Palermo Ser. 2, 20:2–3 (1971), 113–138 | DOI | MR

[6] Potapov D. K., “Nepreryvnye approksimatsii zadachi Goldshtika”, Matem. zametki, 87:2 (2010), 262–266 | DOI | MR | Zbl

[7] Potapov D. K., “Ob odnoi otsenke sverkhu velichiny bifurkatsionnogo parametra v zadachakh na sobstvennye znacheniya dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami”, Differents. uravneniya, 44:5 (2008), 715–716 | MR | Zbl

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

[9] Potapov D. K., Zadachi so spektralnym parametrom i razryvnoi nelineinostyu, Izd-vo IBP, SPb., 2008, 99 pp.

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