Geodesic
On a nonlinear eigenmode problem in semiconductor theory
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 872-880 Cet article a éte moissonné depuis la source Math-Net.Ru

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A model problem in semiconductor physics concerning the natural electrical oscillations in a semiconductor with allowance for strong dissipation and negative differential conductivity is considered. This is a nonlinear boundary value problem, and its solvability is proved by applying S. I. Pohozaev's method of spherical fibering. 
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M. O. Korpusov; A. G. Sveshnikov. On a nonlinear eigenmode problem in semiconductor theory. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 5, pp. 872-880. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_5_a9/

[1] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0$”, Dokl. RAN, 165:1 (1965), 36

[2] Pokhozhaev S. I., “O sobstvennykh funktsiyakh kvazilineinykh ellipticheskikh zadach”, Matem. sb., 82:2 (1970), 192

[3] Kuzin I., Pohozaev S., Entire solutions of semilinear elliptic equations, Nonlinear Different. Equations and their Applic., 33, Birkhäuser, Basel, 1997

[4] Skrypnik I. V., Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990

[5] Klimov V. S., “O funktsionalakh s beskonechnym chislom kriticheskikh znachenii”, Matem. sb., 100:1(5) (1976), 102–116

[6] Lyusternik L. A., Shnirelman L. G., Topologicheskie metody v variatsionnykh zadachakh, Gosizdat, M., 1930

[7] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhteorizdat, M., 1956

[8] Drabek P., Milota Y., Methods of nonlinear analisys. Applications to differential equations, Birkhäser, Basel, 2007, 575 pp.

[9] Ambrosetti A., Rabinowitz P. H., “Dual variational methods in critical point theory and applications”, J. Different. Equations, 14 (1973), 349–381

[10] Clark C. D., “A variant of the Lusternik–Schnirelman theory”, Indiana Univ. Math. J., 22:1 (1972), 65–74

[11] Pokhozhaev S. I., “O metode rassloeniya resheniya nelineinykh kraevykh zadach”, Tr. MIAN SSSR, 192, M., 1990, 146–163

[12] Landau L. D., Lifshits E. M., Elektrodinamika sploshnykh sred. Teoreticheskaya fizika, v. 8, Nauka, M., 1992