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Three methods for the study of semilinear equations at resonance. (English) Zbl 0828.47054

Summary: Three methods for the study of the solvability of semilinear equations with noninvertible linear parts are compared: the alternative method, the continuation method of Mawhin and a new perturbation method. Some extensions of the last method and applications to differential equations in Banach spaces are presented.

MSC:

47J05 Equations involving nonlinear operators (general)
47E05 General theory of ordinary differential operators
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