Infinitely Many Nodal Solutions for Kirchhoff-Type Equations with Non-odd Nonlinearity

• Fuyi Li ^[1] ; Cui Zhang ^[1] ; Zhanping Liang ^[1]
  1. [1] Shanxi University

     Shanxi University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 1, 2024
• Idioma: inglés
• Enlaces
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• Resumen

  • In this study, we investigate the existence of infinitely many radial sign-changing solutions with nodal properties for a class of Kirchhoff-type equations possessing non-odd nonlinearity. By combining variational methods and analysis techniques, we prove that for any positive integer k, the equation has a radial solution that changes signs exactly k times. Furthermore, we demonstrate that the energy of such solutions is an increasing function of k. Owing to the inherent characteristics of these equations, the methods used herein significantly differ from those used in the existing literature. Particularly, we discover a unified method to obtain infinitely many radial sign-changing solutions with nodal properties for local and nonlocal problems.

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