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Uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball ∗
  • Zhanping Liang,
  • Fuyi Li,
  • Xiaoting Li
Zhanping Liang
Shanxi University School of Mathematics

Corresponding Author:[email protected]

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Fuyi Li
Shanxi University School of Mathematics
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Xiaoting Li
Shanxi University School of Mathematics
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Abstract

In this paper, we study the uniqueness of nodal radial solutions to nonlinear elliptic equations in the unit ball in R 3 . Under suitable conditions, we prove that, for any given positive integer k, the problem we considered has at most one solution possessing exactly k−1 nodes. Together with the results presented by Nagasaki [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 36 (2): 211–232, 1989] and Tanaka [Proc. Roy. Soc. Edinburgh Sect. A. 138 (6): 1331–1343, 2008], we can prove that more types of nonlinear elliptic equations have the uniqueness of nodal radial solutions.
19 Sep 2023Submitted to Mathematical Methods in the Applied Sciences
19 Sep 2023Submission Checks Completed
19 Sep 2023Assigned to Editor
27 Sep 2023Review(s) Completed, Editorial Evaluation Pending
04 Nov 2023Reviewer(s) Assigned