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Chapter 15 is devoted to the proof of Theorem 1.10 . Namely, we prove that the semilinear Robin problem ( 1.2 ) is uniquely solvable for \(\lambda \) sufficiently large if \(0 < \varepsilon < (1/(1+\sqrt {1-m}))^{2}\) under the conditions (H.1) and (H.2) (see Fig. 1.8 ). Our proof of Theorem 1.10 is based on a method inspired by Wiebers (Math Ann 270:555–570, 1985).

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Proof of Theorem 1.10 (Unique Solvability for \(\lambda \) Sufficiently Large)

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  • 发表日期：

    2025年

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  • Kazuaki Taira

摘要

Chapter 15 is devoted to the proof of Theorem 1.10 . Namely, we prove that the semilinear Robin problem ( 1.2 ) is uniquely solvable for \(\lambda \) sufficiently large if \(0 < \varepsilon < (1/(1+\sqrt {1-m}))^{2}\) under the conditions (H.1) and (H.2) (see Fig. 1.8 ). Our proof of Theorem 1.10 is based on a method inspired by Wiebers (Math Ann 270:555–570, 1985).