Browsing by Author "Kim, Seunghyeok"
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- ItemA non-compactness result on the fractional Yamabe problem in large dimensions(2017) Kim, Seunghyeok; Musso Polla, Mónica; Wei, Juncheng; Wei, Juncheng
- ItemClassification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents(2017) Choi, Woocheol; Kim, SeunghyeokWe study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined in terms of either the spectra of the Dirichlet Laplacian or the integral representation. As a consequence, we classify the asymptotic behavior of all finite energy solutions. Our method also provides a simple and unified approach to deal with the classical (local) Lane-Emden-Fowler equation for any dimension >2.
- ItemExistence theorems of the fractional yamabe problem(2018) Kim, Seunghyeok; Musso Polla, Mónica; Wei, Juncheng
- ItemQualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2016) Choi, Woocheol; Kim, Seunghyeok; Lee, Ki AhmThe objective of this paper is to obtain qualitative characteristics of multi-bubble solutions to the Lane-Emden-Fowler equations with slightly subcritical exponents given any dimension n >= 3. By examining the linearized problem at each m-bubble solution, we provide a number of estimates on the first (n + 2)m-eigenvalues and their corresponding eigenfunctions. Specifically, we present a new and unified proof of the classical theorems due to Bahri-Li-Rey (1995) [2] and Rey (1999) [24] which state that if n >= 4 or n = 3, respectively, then the Morse index of a multi-bubble solution is governed by a certain symmetric matrix whose component consists of a combination of Green's function, the Robin function, and their first and second derivatives. (C) 2016 Elsevier Inc. Ali rights reserved.
- ItemSUPERCRITICAL PROBLEMS IN DOMAINS WITH THIN TOROIDAL HOLES(2014) Kim, Seunghyeok; Pistoia, AngelaIn this paper we study the Lane-Emden-Fowler equation