Topological degree theories and nonlinear operator equations in Banach spaces (Q943671)

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scientific article; zbMATH DE number 5323989
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Topological degree theories and nonlinear operator equations in Banach spaces
scientific article; zbMATH DE number 5323989

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    Topological degree theories and nonlinear operator equations in Banach spaces (English)
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    10 September 2008
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    Let \(X\) be a real Banach space, \(G_1\), \(G_2\) open and bounded such that \(0\in G_2\subset\bar{G}_2\subset G_1\). Let \(T:D(T)\to X\) be accretive such that \(0\in D(T)\) and \(T(0)=0\). Let \(C:D(C)\to X\) be compact or continuous and bounded with the resolvents of \(T\) compact. The authors use various degree theories to find zeros of \(T+C\) in \(D(T+C)\cap(G_1\setminus G_2)\). As a matter of fact, the article contains much more results: the range space may be \(X^*\) instead of \(X\) and \(C\) may belong to more complicated classes of operators. There is a short application to partial differential equations.
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    maximal monotone operators
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    \(m\)-accretive operators
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    compact perturbations
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    compact resolvents
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    excision property
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    Leray-Schauder degree theory
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    Kartsatos-Skrypnik degree theory
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    nonzero solutions
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