Geodesic
Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory
Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 287-301.

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

In this paper, we study the structural and approximative properties of sets admitting an upper semicontinuous acyclic selection from an almost-best approximation operator. We study the questions of nonunique solvability of a nonlinear inhomogeneous Dirichlet problem on the basis of these properties. 
@article{MZM_2004_75_2_a11,
     author = {I. G. Tsar'kov},
     title = {Nonunique {Solvability} of {Certain} {Differential} {Equations} and {Their} {Connection} with {Geometric} {Approximation} {Theory}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {287--301},
     publisher = {mathdoc},
     volume = {75},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a11/}
}
TY  - JOUR
AU  - I. G. Tsar'kov
TI  - Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory
JO  - Matematičeskie zametki
PY  - 2004
SP  - 287
EP  - 301
VL  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a11/
LA  - ru
ID  - MZM_2004_75_2_a11
ER  - 
%0 Journal Article
%A I. G. Tsar'kov
%T Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory
%J Matematičeskie zametki
%D 2004
%P 287-301
%V 75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a11/
%G ru
%F MZM_2004_75_2_a11
I. G. Tsar'kov. Nonunique Solvability of Certain Differential Equations and Their Connection with Geometric Approximation Theory. Matematičeskie zametki, Tome 75 (2004) no. 2, pp. 287-301. http://geodesic.mathdoc.fr/item/MZM_2004_75_2_a11/

[1] Stinrod N., Eilenberg S., Osnovaniya algebraicheskoi topologii, Fizmatgiz, M., 1958

[2] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, 1958, M.

[3] Levinson N., “Positive eigenfunctions for $\triangle u+\lambda f(u)=0$”, Arch. Rat. Mech. and Analysis, 11:3 (1962), 258–272 | DOI | MR | Zbl

[4] Krasnoselskii M. A., Stetsenko V. Ya., “O nekotorykh nelineinykh zadachakh, imeyuschikh mnogo reshenii”, Sib. matem. zh., 4:1 (1963), 120–137 | MR

[5] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0$”, Dokl. AN SSSR, 165:1 (1965), 36–39 | Zbl

[6] Pokhozhaev S. I., “O odnom podkhode k nelineinym uravneniyam”, Dokl. AN SSSR, 247:6 (1979), 1327–1331 | MR | Zbl

[7] Begle T. G., “The Vietoris mapping theorem for bicompact spaces”, Ann. of Math., 51:3 (1950), 534–543 | DOI | MR | Zbl

[8] Borsuk K., Teoriya retraktov, Mir, M., 1971 | MR

[9] Tsarkov I. G., “O svyaznosti nekotorykh klassov mnozhestv v banakhovykh prostranstvakh”, Matem. zametki, 40:2 (1986), 174–196 | MR

[10] Tsarkov I. G., “Svoistva mnozhestv, obladayuschikh nepreryvnoi vyborkoi iz operatora $P^\delta$”, Matem. zametki, 48:4 (1990), 122–131 | MR