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Funktsional'nyi Analiz i ego Prilozheniya, 2016, Volume 50, Issue 1, Pages 38–46
DOI: https://doi.org/10.4213/faa3221 (Mi faa3221) 		 
How to Approach Nonstandard Boundary Value Problems

B. D. Gel'man

Voronezh State University
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DOI: https://doi.org/10.4213/faa3221
Abstract: A new approach to nonstandard boundary value problems is suggested. For such problems, we construct equivalent inclusions with surjective operators and study the solvability of these inclusions. The paper consists of two parts. The first part deals with problems in which the right-hand side of the equation is a Lipschitz mapping (Section 3); in the second part (Section 4), this mapping is completely continuous with respect to a surjective operator $A$. The paper also gives examples of how our theorems can be applied when studying nonstandard boundary value problems.
Keywords: closed surjective operator, set-valued contraction mapping, differential equation, topological dimension.
Received: 05.02.2015
English version:
Functional Analysis and Its Applications, 2016, Volume 50, Issue 1, Pages 31–38
DOI: https://doi.org/10.1007/s10688-016-0125-4
Bibliographic databases:
Document Type: Article
UDC: 517.988.6
Language: Russian
Citation: B. D. Gel'man, “How to Approach Nonstandard Boundary Value Problems”, Funktsional. Anal. i Prilozhen., 50:1 (2016), 38–46; Funct. Anal. Appl., 50:1 (2016), 31–38
Citation in format AMSBIB
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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