Geodesic
On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 86-88.

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

We consider the question of existence of Dirichlet’s problem solution for the Laplace equation with a spectral parameter and discontinuous on a phase variable nonlinearity. Using the variational method, we prove a theorem about a number of solutions. We result an example of discontinuous nonlinearity that satisfies to conditions of the theorem for which there is unique semiregular solution of this boundary problem. 
@article{DVMG_2012_12_1_a6,
     author = {D. K. Potapov},
     title = {On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {86--88},
     publisher = {mathdoc},
     volume = {12},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/}
}
TY  - JOUR
AU  - D. K. Potapov
TI  - On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2012
SP  - 86
EP  - 88
VL  - 12
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/
LA  - ru
ID  - DVMG_2012_12_1_a6
ER  - 
%0 Journal Article
%A D. K. Potapov
%T On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2012
%P 86-88
%V 12
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/
%G ru
%F DVMG_2012_12_1_a6
D. K. Potapov. On number of solutions for one class of elliptic equations with a spectral parameter and discontinuous nonlinearity. Dalʹnevostočnyj matematičeskij žurnal, Tome 12 (2012) no. 1, pp. 86-88. http://geodesic.mathdoc.fr/item/DVMG_2012_12_1_a6/

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

[2] D. K. Potapov, “O suschestvovanii lucha sobstvennykh znachenii dlya uravnenii ellipticheskogo tipa s razryvnymi nelineinostyami v kriticheskom sluchae”, Vestn. S.-Peterb. un-ta, Ser. 10. Prikladnaya matematika. Informatika. Protsessy upravleniya. Vyp. 4, 2004, 125–132

[3] D. K. Potapov, “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

[4] M. A. Krasnoselskii, A. V. Pokrovskii, “Pravilnye resheniya uravnenii s razryvnymi nelineinostyami”, Dokl. AN SSSR, 226:3 (1976), 506–509 | MR

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

[6] K. C. Chang, “Variational methods for non-differentiable functionals and their applications to partial differential equations”, J. Math. Anal. and Appl., 80:1 (1981), 102–129 | DOI | MR | Zbl

[7] S. Agmon, A. Duglis, L. Nirenberg, Otsenki reshenii ellipticheskikh uravnenii vblizi granitsy, Izd-vo inostr. lit., M., 1962, 208 pp.

[8] I. I. Vainshtein, “Reshenie dvukh dualnykh zadach o skleike vikhrevykh i potentsialnykh techenii variatsionnym metodom M. A. Goldshtika”, Zhurn. SFU, Ser. Matem. i fiz. Vyp. 3, v. 4, 2011, 320–331