Existence of normalized solutions for the coupled Hartree–Fock type system

Wang, Jun

doi:10.1002/mana.201900230

Cited by 10 publications

(2 citation statements)

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“…The results on the existence and properties of normalized solutions of (1.4) are few, and as we know, the nonlinearities of (1.4) in the existing related results [10,22,23] are all of subcritical growth in the sense of Hardy-Littlewood-Sobolev inequality, i.e. p, q, r 1 , r 2 < 2 * µ .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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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Section: Introduction and Main Resultsmentioning

confidence: 99%

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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“…Recently, the normalized solutions of nonlinear Schrödinger equations and systems has attracted many researchers, see more details [2,3,4,5,6,12,14,15,18,28,29,32]. In particular, for s = 1, Wang in [30] considered the system (1.1) with 1+ α+2s N < p, q < N +α N −2s , by min-max principle and Liouville type theorem, he gave the existence of normalized solutions. Wang and Yang in [31] considered (1.1) with L 2 − critical exponent, they gave the existence and asymptotic behaviours of normalized solutions.…”

Section: Introductionmentioning

confidence: 99%