Topological degree theories and nonlinear operator equations in Banach spaces. (English) Zbl 1142.47346
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.
Reviewer: Christian Fenske (Gießen)
MSC:
| 47H11 | Degree theory for nonlinear operators |
| 47B44 | Linear accretive operators, dissipative operators, etc. |
| 47H05 | Monotone operators and generalizations |
Keywords:
maximal monotone operators; \(m\)-accretive operators; compact perturbations; compact resolvents; excision property; Leray-Schauder degree theory; Kartsatos-Skrypnik degree theory; nonzero solutionsReferences:
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