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arXiv · 2511.11543

Entire Nodal Solutions with Prescribed Symmetry to Caffarelli-Kohn-Nirenberg Equations

Edward Chernysh
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Abstract

We establish the existence of sign-changing entire solutions to weighted critical $p$-Laplace equations of the Caffarelli-Kohn-Nirenberg type. In doing so, we investigate classes of symmetry and show that, for suitable symmetry configurations, there exists a non-trivial solution which changes sign and respects the corresponding prescribed symmetry. In addition, we describe conditions under which these symmetry-types are incompatible. Especially, we demonstrate the existence of entire nodal solutions for an infinite number of distinct symmetry types.

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Edward Chernysh. 2025-11-14. Entire Nodal Solutions with Prescribed Symmetry to Caffarelli-Kohn-Nirenberg Equations. https://arxiv.org/abs/2511.11543

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