Geodesic
How to Approach Nonstandard Boundary Value Problems
Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 38-46

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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. 
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     author = {B. D. Gel'man},
     title = {How to {Approach} {Nonstandard} {Boundary} {Value} {Problems}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a2/}
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B. D. Gel'man. How to Approach Nonstandard Boundary Value Problems. Funkcionalʹnyj analiz i ego priloženiâ, Tome 50 (2016) no. 1, pp. 38-46. http://geodesic.mathdoc.fr/item/FAA_2016_50_1_a2/