Existence and asymptotic behavior of normalized ground states for Sobolev critical Schrödinger systems

Bartsch, Thomas; Li, Houwang; Zou, Wenming

doi:10.1007/s00526-022-02355-9

Cited by 13 publications

(4 citation statements)

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“…Regarding the existence and qualitative properties of normalized solutions of (1.3) we refer the reader to [1,4,5,12] for Sobolev subcritical case, and [2] for Sobolev critical case. In [2], Bartsch et al considered the nonlinear Schrödinger system (1.3) with 2r 1 = 2r 2 = 2 * := 2N/(N − 2) by assuming N ∈ {3, 4}, p, q > 1 and p + q < 2 * . They proved that a normalized ground state does not exist for ν < 0.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…Inspired by the work in [2] for critical Schrödinger system with local nonlinearity, in the present paper we aim to study the existence and asymptotic behavior of normalized solutions of critical nonlocal Choquard system…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…To give the compactness lemma, we need a regularity result. Different from [2], the nonlocal term leads that the integrability of solutions of the system (1.8) should be improved. Firstly let us recall an important inequality for nonlocal nonlinearities by Moroz and Van Schaftingen [19].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

“…In the super-critical case, due to the non-homogeneous and non-locality of the nonlinear term, it is difficult for us to use the Riesz's rearrangement inequality (see [18]) to obtain m ν (a, b) = m r,ν (a, b). Consequently, different from [2] where only one threshold was considered, it is necessary to introduce two thresholds as follows…”

Section: Lemma 32 (Improved Integrability Of Solutions Of a Nonlocal ...mentioning

confidence: 99%

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Introduction to the Department of Cardiology in Nanjing First Hospital of Nanjing Medical University, China

Zhang

Chen

2020

European Heart Journal

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Reclosure of ruptured incision after peroral endoscopic myotomy using endoloops and metallic clipsSince Inoue et al. introduced peroral endoscopic myotomy (POEM) into a clinic to treat esophageal achalasia in 2010, the procedure has been carried out in many countries around the world. 1 As more and more POEM is being done, associated technical difficulties and complications may occur. 2 To our knowledge, the present study is the first to report incision rupture after POEM.A 37-year-old man presented to our academic center after experiencing 25 years of dysphagia and 2 months of exacerbation. Barium swallow examination and esophageal manometry diagnosed the patient with type I esophageal achalasia and he agreed to receive POEM.POEM was carried out using the standard technique. After the operation, the patient received routine postoperative care. On the third day after the procedure, the patient had a fever (38.9°C, white blood cell count 18.24 × 10 9 /L, % neutrophils 95.3%) and X-ray showed the absence of several metal clips at the proximal end of the longitudinal incision which revealed the incision rupture.Gastroesophageal endoscopy showed that the middle and proximal parts of the incision was ruptured. It was not possible to reclose the incision with routine clips because of the swollen mucosa around the defect. On endoscopy, an endoloop was inserted and snared the remaining clips in the distal part. In the middle, four clips were anchored onto the defect margins at full thickness and another endoloop was inserted to snare the clips tightly. The same procedure was done in the proximal part (Figs 1,2). After monitoring the patient's condition for several days, he was discharged without any complaints or complications.In the present study, we propose reclosure of a mucosal incision after POEM using conventional endoloops and hemostatic clips. It could reclose the incision regardless of the swollen tissue or the size of the longitudinal incision.

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