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A Class of Semilinear Hypoelliptic Robin Problems at Resonance

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  • Kazuaki Taira

Abstract

(1) This paper is devoted to the study of a class of semilinear hypoelliptic (degenerate) Robin problems at resonance that include semilinear regular Robin problems at resonance. (2) We give a rigorous proof of main theorems in the framework of Hölder spaces, which is heavily based on the Lp$L^{p}$ theory of linear elliptic boundary value problems. In point of fact, we develop a modern version of the classical Lyapunov–Schmidt procedure, the global inversion theorem, and the intermediate‐value theorem from scratch in the framework of Lp$L^{p}$ Sobolev spaces. (3) We extend an earlier theorem due to Landesman and Lazer to the hypoelliptic case. (4) The main purpose of this paper is to understand the essence of a modern version of the classical Lyapunov–Schmidt procedure at resonance through a concrete approach to semilinear hypoelliptic Robin problems.

Suggested Citation

  • Kazuaki Taira, 2026. "A Class of Semilinear Hypoelliptic Robin Problems at Resonance," Mathematische Nachrichten, Wiley Blackwell, vol. 299(5), pages 1085-1124, May.
    • Handle: RePEc:bla:mathna:v:299:y:2026:i:5:p:1085-1124
    DOI: 10.1002/mana.70129
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