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Existence theorems for nonlinear operator equation \(Lu+Nu=f\) and some properties of the set of solutions. (English) Zbl 0744.34025
Author’s abstract: “We give an existence theorem and study the compactness and connectedness of the set of solutions to the operator equation \(Lu+Nu=f\). The linear operator \(L\) is not necessarily invertible and the nonlinear operator \(N\) is continuous and bounded. The proofs are based on a topological degree and Leray-Schauder techniques”.
Reviewer: J.F.Toland (Bath)
MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
47J05 Equations involving nonlinear operators (general)
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References:
[1] CESARI L.: Functional analysis and Galerkin’s method. Michigan Math. J. 11 (1964), 385-414. · Zbl 0192.23702 · doi:10.1307/mmj/1028999194
[2] FUČÍK S., KUFNER A.: Nelineární diferenciální rovnice. SNTL, Praha, 1978. · Zbl 0474.35001
[3] GREGUŠ M., ŠVEC M., ŠEDA V.: Obyčajné diferenciálné rovnice. Alfa, Bratislava, 1985.
[4] KODDINGTON E. A., LEVINSON N.: Teorija obyknovennych differencial’nych uravnenij. Izdat. Inostr. lit., Moskva, 1958.
[5] MAWHIN J.: Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces. J .Differential Equations 12 (1972), 610-636. · Zbl 0244.47049 · doi:10.1016/0022-0396(72)90028-9
[6] TAYLOR A. E.: Úvod do funkcionální analysy. Academia, Praha, 1973.
[7] WARD J. R.: Existence theorems for nonlinear boundary value problems at resonance. J. Differential Equations 35 (1980), 232-247. · Zbl 0447.34015 · doi:10.1016/0022-0396(80)90041-8
[8] ZEIDLER E.: Vorlesungen über nichtlineare Funktionalanalysis I. Teubner Verlag, Leipzig, 1976. · Zbl 0326.47053
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