Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs

Louis Jeanjean; Linjie Song

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arXiv · 2501.14642

Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs

Louis Jeanjean·Linjie Song

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Abstract

This paper is devoted to the existence of multiple sign-changing solutions of prescribed mass for a mass-supercritical nonlinear Schr\"odinger equation set on a compact metric graph. In particular, we obtain, in the supercritical mass regime, the first multiplicity result for prescribed mass solutions on compact metric graphs. As a byproduct, we prove that any eigenvalue of the associated linear operator is a bifurcation point. Our approach relies on the introduction a new kind of link and on the use of gradient flow techniques on a constraint. It can be transposed to other problems posed on a bounded domain.

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Louis Jeanjean, Linjie Song. 2025-01-24. Sign-changing prescribed mass solutions for $L^2$-supercritical NLS on compact metric graphs. https://arxiv.org/abs/2501.14642

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