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Carriao, Paulo Cesar,Lisboa, Narciso Horta,Miyagaki, Olimpio Hiroshi Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v>0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.
Paulo Cesar Carriao,Olimpio Hiroshi Miyagaki,Narciso Horta Lisboa 대한수학회 2013 대한수학회보 Vol.50 No.3
We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system (S) [수식], where ε is a small positive parameter; V1, V2 ∈ C0(RN, [0,1)) and K 2 C0(RN, (0,∞)) are radially symmetric potentials; Q is a (p + 1)- homogeneous function and p is subcritical, that is, 1 < p < 2∗ −1, where 2∗ = 2N/(N − 2) is the critical Sobolev exponent for N ≥ 3.
Taro Shibuki,Kei Okumura,Masanari Sekine,Ikuhiro Kobori,Aki Miyagaki,Yoshihiro Sasaki,Yuichi Takano,Yusuke Hashimoto 대한소화기내시경학회 2023 Clinical Endoscopy Vol.56 No.6
Background/Aims: Covered self-expandable metallic stents (cSEMS) have become popular for endoscopic ultrasound-guided hepati-cogastrostomy with transmural stenting (EUS-HGS). We compared the time to recurrent biliary obstruction (TRBO), complications,and reintervention rates between EUS-HGS using plastic stent (PS) and cSEMS in patients with unresectable malignancies at multi-center institutions in Japan. Methods: Patients with unresectable malignant biliary obstruction who underwent EUS-HGS between April 2015 and July 2020 at anyof the six participating facilities were enrolled. Primary endpoint: TRBO; secondary endpoints: rate of complications other than recur-rent biliary obstruction and technical success rate of reintervention were evaluated. Results: PS and cSEMS were used for EUS-HGS in 109 and 43 patients, respectively. The TRBO was significantly longer in the cSEMSgroup than in the PS group (646 vs. 202 days). Multivariate analysis identified two independent factors associated with a favorableTRBO: combined EUS-guided antegrade stenting with EUS-HGS and the use of cSEMS. No significant difference was observed in therate of complications other than recurrent biliary obstruction between the two groups. The technical success rate of reintervention was85.7% for PS and 100% for cSEMS (p=0.309). Conclusions: cSEMS might be a better option for EUS-HGS in patients with unresectable malignancies, given the longer TRBO.