Results 11 to 20 of about 41 (41)
Local properties of maps of the ball
Abstract and Applied Analysis, Volume 2003, Issue 2, Page 75-81, 2003., 2003 Let f be an essential map of Sn−1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B¯n into ℝn. Then, for every interior point y of Bn, there exists a point x in f−1(y) such that the image of no neighborhood of x is contained in a coordinate half space with y on its boundary.
Yakar Kannai
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Properness and topological degree for general elliptic operators
Abstract and Applied Analysis, Volume 2003, Issue 3, Page 129-181, 2003., 2003 The paper is devoted to general elliptic operators in Hölder spaces in bounded or unbounded domains. We discuss the Fredholm property of linear operators and properness of nonlinear operators. We construct a topological degree for Fredholm and proper operators of index zero.
V. Volpert, A. Volpert
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Approximation structures and applications to evolution equations
Abstract and Applied Analysis, Volume 2003, Issue 12, Page 685-696, 2003., 2003 We discuss various properties of the nonlinear A‐proper operators as well as a generalized Leray‐Schauder principle. Also, a method of approximating arbitrary continuous operators by A‐proper mappings is described. We construct, via appropriate Browder‐Petryshyn approximation schemes, approximative solutions for linear evolution equations in Banach ...
Adrian Duma, Cristian Vladimirescu
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Eigenvalue Problems for Fredholm Operators with Set-Valued Perturbations
Advanced Nonlinear Studies, 2020 By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator.
Benevieri Pierluigi, Iannizzotto Antonio
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Periodic solutions of nonlinear vibrating beams
Abstract and Applied Analysis, Volume 2003, Issue 14, Page 823-841, 2003., 2003 The aim of this paper is to prove new existence and multiplicity results for periodic semilinear beam equation with a nonlinear time‐independent perturbation in case the period is not prescribed. Since the spectrum of the linear part varies with the period, the solvability of the equation depends crucially on the period which can be chosen as a free ...
J. Berkovits, H. Leinfelder, V. Mustonen
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On boundary value problems for degenerate differential inclusions in Banach spaces
Abstract and Applied Analysis, Volume 2003, Issue 13, Page 769-784, 2003., 2003 We consider the applications of the theory of condensing set‐valued maps, the theory of set‐valued linear operators, and the topological degree theory of the existence of mild solutions for a class of degenerate differential inclusions in a reflexive Banach space.
Valeri Obukhovskii, Pietro Zecca
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High Multiplicity and Chaos for an Indefinite Problem Arising from Genetic Models
Advanced Nonlinear Studies, 2020 We deal with the periodic boundary value problem associated with the parameter-dependent second-order nonlinear differential ...
Boscaggin Alberto +2 more
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Existence problems for homoclinic solutions
Abstract and Applied Analysis, Volume 7, Issue 1, Page 1-27, 2002., 2002 The problem x˙=f(t,x), x(−∞)=x(+∞), where x(±∞) : = limt→±∞x(t) ∈ ℝn, is considered. Some existence results for this problem are established using the fixed point method and topological degree theory.
Cezar Avramescu
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A Fredholm alternative for quasilinear elliptic equations with right-hand side measure
Advances in Nonlinear Analysis, 2016 We consider a quasilinear elliptic equation with right-hand side measure, which does not satisfy the usual coercivity assumption. We prove an existence result in the line of the Fredholm alternative. For this purpose we develop a variant of degree theory
Colturato Michele, Degiovanni Marco
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On coincidence index for multivalued perturbations of nonlinear Fredholm maps and some applications
Abstract and Applied Analysis, Volume 7, Issue 6, Page 295-322, 2002., 2002 We define a nonoriented coincidence index for a compact, fundamentally restrictible, and condensing multivalued perturbations of a map which is nonlinear Fredholm of nonnegative index on the set of coincidence points. As an application, we consider an optimal controllability problem for a system governed by a second‐order integro‐differential equation.
Valeri Obukhovskii +2 more
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