Results 11 to 20 of about 192 (65)
Semilinear systems with a multi-valued nonlinear term
Open Mathematics, 2017 Introducing a topological degree theory, we first establish some existence results for the inclusion h ∈ Lu − Nu in the nonresonance and resonance cases, where L is a closed densely defined linear operator on a Hilbert space with a compact resolvent and ...
Kim In-Sook, Hong Suk-Joon
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Global Perturbation of Nonlinear Eigenvalues
Advanced Nonlinear Studies, 2021 This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏:[a,b]×[c,d]→Φ0(U,V){\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)}, (λ,μ)↦𝔏(λ,μ){(\lambda,\mu)\mapsto\mathfrak ...
López-Gómez Julián +1 more
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Shooting with degree theory: Analysis of some weighted poly-harmonic systems [PDF]
, 2014 In this paper, the author establishes the existence of positive entire solutions to a general class of semilinear poly-harmonic systems, which includes equations and systems of the weighted Hardy--Littlewood--Sobolev type.
Villavert, John
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An index formula for the degree of (S)+‐mappings associated with one‐dimensional p‐Laplacian
Abstract and Applied Analysis, Volume 2004, Issue 11, Page 981-995, 2004., 2004 The topological degree for (S)+‐mappings concerning a nonlinear eigenvalue problem associated with one‐dimensional p‐Laplacian is evaluated. The result is applied to a variational inequality, where the multiple existence of solutions is discussed.
Jun Kobayashi, Mitsuharu Ôtani
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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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