Nonunique solvability of certain differential equations and their connection with geometric approximation theory

Mathematical Notes

Volumn 75, Issue 1-2, 2004, Pages 259-271

  Tsar'kov, I G ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Acyclic selection; Almost best approximation operator; Approximative compactness; Inhomogeneous Dirichlet problem; Nonunique solvability of differential equations

Indexed keywords

EID: 3543076357     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:matn.0000015042.89501.ed     Document Type: Article

References (10)

1. N. Steenrod and S. Eilenberg, Foundations of Algebraic Topology, Princeton University Press, Princeton, New Jersey, 1952.
2. M. A. Krasnosel'skii and Ya. B. Rutitskii, Convex Functions and Orlicz Spaces [in Russian], Moscow, 1958.
3. N. Levinson, "Positive eigenfunctions for Δu + λf(u) = 0," Arch. Rat. Mech. and Analysis, 11 (1962), no. 3, 258-272.
4. M. A. Krasnosel'skii and V. Ya. Stetsenko, "On nonlinear problems having many solutions" Sibirsk. Mat. Zh. [Siberian Math. J.], 4 (1963), no. 1, 120-137.
5. S. I. Pokhozhaev, "On the eigenfunctions of the equation Δu + λf(u) = 0," Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 165 (1965), no. 1, 36-39.
6. S. I. Pokhozhaev, "On an approach to nonlinear equations," Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 247 (1979), no. 6, 1327-1331.
7. T. G. Begle, "The Vietoris mapping theorem for bicompact spaces," Ann. of Math., 51 (1950), no. 3, 534-543.
8. K. Borsuk, Theory of Retracts, PWN, Warsaw, 1967; Russian translation, Mir, Moscow, 1971.
9. I. G. Tsar'kov, "On the connectedness of some classes of sets in Banach spaces," Mat. Zametki [Math. Notes], 40 (1986), no. 2, 174-196.
10. δ" Mat. Zametki [Math. Notes], 48 (1990), no. 4, 122-131.