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作者:B. D. Gel’man
来源:[J].Mathematical Notes(IF 0.239), 2017, Vol.101 (5-6), pp.951-959Springer
摘要:... In conclusion, this hybrid theorem is used to study the solvability of operator inclusions for a new class of operators containing all surjective operators. The obtained result is applied to solve the solvability problem for a certain class of control systems determined by a...
作者:B. D. Gel’man
来源:[J].Functional Analysis and Its Applications(IF 0.528), 2019, Vol.53 (1), pp.61-64Springer
摘要:Abstract(#br)The solvability of the equation A ( x ) = f ( x ) on the sphere of a Hilbert space and the dimension of its solution set are studied in the case where A is a closed surjective operator and f is an odd Lipschitz mapping. A kind of analogue of the infinite-dimensional ...
作者:B. D. Gel’man
来源:[J].Functional Analysis and Its Applications(IF 0.528), 2016, Vol.50 (1), pp.31-38Springer
摘要:... 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); ...
作者:B. D. Gel’man
来源:[J].Functional Analysis and Its Applications(IF 0.528), 2018, Vol.52 (2), pp.139-143Springer
摘要:Abstract(#br)A fixed-point theorem is proved for a finite composition of set-valued Lipschitz maps such that the product of their Lipschitz constants is less than 1. The notion of a Lipschitz tuple of (finitely many) set-valued maps is introduced; it is proved that such a tuple h...
作者:Hugo Leiva , Edgar Iturriaga
来源:[J].Applied Mathematics, 2010, Vol.01 (04), pp.265-273Scientific Research Publishing
摘要:In this paper we characterize a broad class of semilinear surjective operators given by the following formula where Z are Hilbert spaces, and is a suitable nonlinear function. First, we give a necessary and sufficient condition for the linear operator to be surjective. Second, we...
作者:Nikolaos S. Papageorgiou , Nikolaos Yannakakis
来源:[J].Proceedings of the Indian Academy of Sciences - Mathematical Sciences(IF 0.191), 1999, Vol.109 (2), pp.211-230Springer
摘要:... Using the theory of maximal monotone operators for reflexive Banach spaces and the Leray-Schauder principle we establish the existence of solutions for both problems.
作者:Edgar Iturriaga , Hugo Leiva
来源:[J].Applied Mathematics, 2010, Vol.1 (4), pp.265-273Airiti
摘要:In this paper we characterize a broad class of semilinear surjective operators GH:V→Z given by the following formula GHw=Gw+H(w), w∈V, where V, Z are Hilbert spaces, G∈L(V,Z) and H:V→Z is a suitable nonlinear function. First, we give a necessary and sufficient conditi...
作者:B. D. Gel’man
来源:[J].Functional Analysis and Its Applications(IF 0.528), 2015, Vol.49 (1), pp.60-63Springer
摘要:Abstract(#br)Operator equations of the form A ( x ) = f ( x ) are studied in the case where A is a closed surjective linear operator and the map f is condensing with respect to A . Not only existence theorems are proved but also the topological dimension of the solution set of su...
作者:Anton R. Schep
来源:[J].Indagationes Mathematicae(IF 0.206), 2014, Vol.25 (2), pp.366-375Elsevier
摘要:... A bounded linear operator T : E → F is an isomorphism on the positive cone of E if and only if T ∗ is almost surjective. A dual version of this theorem holds also. A bounded linear operator T : F → E is almost surjective if and only if T ∗ is an isomorphism on the ...
作者:B. D. Gel’man
来源:[J].Functional Analysis and Its Applications(IF 0.528), 2004, Vol.38 (4), pp.239-242Springer
摘要:Abstract(#br)We study the solvability of the equation a ( x ) = f ( x ) on a sphere in a Banach space, where a is a closed surjective linear operator and f is an odd a -compact map. We also estimate the topological dimension of the solution set and give applications of the corres...

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