24 citations · 56 across the 19 of their papers we have counts for
20 papers
Sign-changing solutions for critical Hamiltonian systems in
Yuxia Guo, Seunghyeok Kim, Angela Pistoia +1
We build infinitely many geometrically distinct non-radial sign-changing solutions for the Hamiltonian-type elliptic systems $$ -Δu =|v|^{p-1}v\ \hbox{in}\ \mathbb{R}^N,\ -Δv =|u|^…
Coron's problem for the critical Lane-Emden system
Sangdon Jin, Seunghyeok Kim
In this paper, we address the solvability of the critical Lane-Emden system \[\begin{cases} -Δu=|v|^{p-1}v &\mbox{in } Ω_ε,\\ -Δv=|u|^{q-1}u &\mbox{in } Ω_ε,\\ u=v=0 &\mbox{on } \p…
Asymptotic analysis on positive solutions of the Lane-Emden system with nearly critical exponents
Seunghyeok Kim, Sang-Hyuck Moon
We concern a family of solutions of the Lane-Emden system on a smooth bounded convex domain in \[\begin…
Infinite-time blowing-up solutions to small perturbations of the Yamabe flow
Seunghyeok Kim, Monica Musso
Under the validity of the positive mass theorem, the Yamabe flow on a smooth compact Riemannian manifold of dimension is known to exist for all time and converges to…
Multiple blowing-up solutions to critical elliptic systems in bounded domains
Seunghyeok Kim, Angela Pistoia
We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogo…
Non-degeneracy for the critical Lane-Emden system
Rupert L. Frank, Seunghyeok Kim, Angela Pistoia
We prove the non-degeneracy for the critical Lane--Emden system for all and such th…
A perturbative approach to non-degeneracy of the Lane-Emden system
Seunghyeok Kim, Angela Pistoia
We consider ground state solutions of the critical Lane-Emden system \[\begin{cases} -Δu = v^p &\text{in } \mathbb{R}^n,\\ -Δv = u^q &\text{in } \mathbb{R}^n,\\ u,v >0\ &\text{in }…
Compactness of scalar-flat conformal metrics on low-dimensional manifolds with constant mean curvature on boundary
Seunghyeok Kim, Monica Musso, Juncheng Wei
We concern -compactness of the solution set of the boundary Yamabe problem on smooth compact Riemannian manifolds with boundary provided that their dimensions are , or…
A compactness theorem of the fractional Yamabe problem, Part I: The non-umbilic conformal infinity
Seunghyeok Kim, Monica Musso, Juncheng Wei
Assume that is an asymptotically hyperbolic manifold, is its conformal infinity, is the geodesic boundary defining function associated to …
Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola
Woocheol Choi, Seunghyeok Kim
The Lane-Emden system is written as \begin{equation*} \begin{cases} -Δu = v^p &\text{in } Ω,\\ -Δv = u^q &\text{in } Ω,\\ u, v > 0 &\text{in } Ω,\\ u = v = 0 &\text{on } \partial Ω…
Conformal metrics with prescribed fractional scalar curvature on conformal infinities with positive fractional Yamabe constants
Seunghyeok Kim
Let be an asymptotically hyperbolic manifold and its conformal infinity. Our primary aim in this paper is to introduce the prescribed fractional scalar…
Minimal energy solutions to the fractional Lane-Emden system, I: Existence and singularity formation
Woocheol Choi, Seunghyeok Kim
This is the first of two papers which study asymptotic behavior of minimal energy solutions to the fractional Lane-Emden system in a smooth bounded domain \[(-Δ)^s u = v^p, \qu…
Existence theorems of the fractional Yamabe problem
Seunghyeok Kim, Monica Musso, Juncheng Wei
Let be an asymptotically hyperbolic manifold and its conformal infinity. This paper is devoted to deduce several existence results of the fractional Yamabe problem on u…
Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents
Woocheol Choi, Seunghyeok Kim
We study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined…
A non-compactness result on the fractional Yamabe problem in large dimensions
Seunghyeok Kim, Monica Musso, Juncheng Wei
Let be an -dimensional asymptotically hyperbolic manifold with a conformal infinity . The fractional Yamabe problem addresses to solve \[P…
On perturbations of the fractional Yamabe problem
Woocheol Choi, Seunghyeok Kim
The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature…
Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents
Woocheol Choi, Seunghyeok Kim, Ki-Ahm Lee
The 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 dime…
Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian
Woocheol Choi, Seunghyeok Kim, Ki-Ahm Lee
In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional L…
Supercritical problems in domains with thin toroidal holes
Seunghyeok Kim, Angela Pistoia
In this paper we study the Lane-Emden-Fowler equation Here $\mathcal D_ε= \mathcal D \…
Boundary towers of layers for some supercritical problems
Seunghyeok Kim, Angela Pistoia
We show that in some suitable torus-like domains D some supercritical elliptic problems have an arbitrary large number of sign-changing solutions with alternate positive and negati…