Strong Instability of Ground States to a Fourth Order Schrödinger Equation

Strong Instability of Ground States to a Fourth Order Schrödinger Equation

In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectu...

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Veröffentlicht in:International mathematics research notices 2019-09, Vol.2019 (17), p.5299-5315
Hauptverfasser: Bonheure, Denis, Castéras, Jean-Baptiste, Gou, Tianxiang, Jeanjean, Louis
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Mathematics
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Zusammenfassung:In this note, we prove the instability by blow-up of the ground state solutions for a class of fourth order Schrödinger equations. This extends the first rigorous results on blowing-up solutions for the biharmonic nonlinear Schrödinger due to Boulenger and Lenzmann [8] and confirm numerical conjectures from [1–3, 11].
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnx273