## 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.

### MSC:

 47H11 Degree theory for nonlinear operators 47B44 Linear accretive operators, dissipative operators, etc. 47H05 Monotone operators and generalizations
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### References:

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