Nodal solutions to Paneitz-type equations

Nodal solutions to Paneitz-type equations

On a closed Riemannian manifold (Mn,g) with a proper isoparametric function f we consider the equation Δ2u−αΔu+βu=uq, where α and β are positive constants satisfying that α2≥4β. We let m be the minimum of the dimensions of the focal varieties of f and qf=n−m+4n−m−4, qf=∞ if n≤m+4. We prove the exist...

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Veröffentlicht in:Journal of mathematical analysis and applications 2025-05, Vol.545 (1), p.129203, Article 129203
Hauptverfasser: Julio-Batalla, Jurgen, Petean, Jimmy
Format: Artikel
Sprache:eng
Schlagworte:
Critical Sobolev exponent
Isoparametric functions
Nodal solutions
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Zusammenfassung:On a closed Riemannian manifold (Mn,g) with a proper isoparametric function f we consider the equation Δ2u−αΔu+βu=uq, where α and β are positive constants satisfying that α2≥4β. We let m be the minimum of the dimensions of the focal varieties of f and qf=n−m+4n−m−4, qf=∞ if n≤m+4. We prove the existence of infinitely many nodal solutions of the equation assuming that 1
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.129203