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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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