What does this research mean for the field?

For the fractional Kirchhoff equation with L2-supercritical perturbations, the number of normalized solutions is directly related to the topology of the set where the potential attains its minimum value. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

Investigate the multiplicity of normalized solutions with prescribed mass for fractional autonomous and non-autonomous Kirchhoff equations under mass supercritical growth conditions.

August 24, 2026Bulletin of Mathematical SciencesOpen Access

Multiple normalized solutions for the fractional autonomous and non-autonomous Kirchhoff equation: the L 2 -supercritical case

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Investigate the multiplicity of normalized solutions with prescribed mass for fractional autonomous and non-autonomous Kirchhoff equations under mass supercritical growth conditions.
Formulated the non-local fractional problem using variational frameworks with a prescribed mass constraint, treating the parameter as a Lagrange multiplier.
Analyzed the topological properties of the set where the potential function reaches its minimum value under mass supercritical conditions.
Proved that the number of normalized solutions is governed by the topology of the set where the potential attains its minimum.
Demonstrated the existence of multiple normalized ground state solutions concentrating at a potential well for fractional Kirchhoff equations with L2-supercritical perturbations.

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Implication

Mathematical analysis reveals multiple normalized solutions for fractional Kirchhoff equations, linking solution counts to potential well topology.

Cite This Study

Meng et al. (2026) studied this question.

synapsesocial.com/papers/6a8c009fbca056c88e6df5f4 https://doi.org/10.1142/s1664360726500207

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Implication

Mathematical analysis reveals multiple normalized solutions for fractional Kirchhoff equations, linking solution counts to potential well topology.

Multiple normalized solutions for the fractional autonomous and non-autonomous Kirchhoff equation: the L 2 -supercritical case

Key Points

Discussion

Implication

Cite This Study

Multiple normalized solutions for the fractional autonomous and non-autonomous Kirchhoff equation: the L 2 -supercritical case

Key Points

Discussion

Implication

Cite This Study

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