## On the eigenvalue problem for perturbations of nonlinear accretive and monotone operators in Banach spaces.(English)Zbl 0864.47028

The paper deals with the solvability of the equation $O\in Tx-\lambda Cx$ with respect to $$(\lambda,x)\in (0,+\infty)\times D/(T)$$ with $$x\neq 0$$. The operator $$C$$ is compact and $$T$$ satisfies at least some type of monotonicity or accretiveness assumption. The results are an extension of results by Fitzpatrick and Petryshyn. The main tool used is a generalized Leray-Schauder degree theory. Possible extensions and applications of the results are indicated in the last paragraph.

### MSC:

 47H06 Nonlinear accretive operators, dissipative operators, etc. 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems 47H05 Monotone operators and generalizations
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### References:

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