6 papers · 1 filter
On the Brezis-Nirenberg problem for the -Laplacian
Ky Ho, Kanishka Perera, Inbo Sim
We prove some existence and nonexistence results for a class of critical -Laplacian problems in a bounded domain. Our results extend and complement those in the literature f…
On sufficient "local" conditions for existence results to generalized -Laplace equations involving critical growth
Ky Ho, Inbo Sim
In this paper, we study the existence of multiple solutions to a generalized -Laplace equation with two parameters involving critical growth. More precisely, we give suff…
Properties of eigenvalues and some regularities on fractional -Laplacian with singular weights
Ky Ho, Inbo Sim
We provide fundamental properties of the first eigenpair for fractional -Laplacian eigenvalue problems under singular weights, which is related to Hardy type inequality, and als…
Positive solutions of semipositone elliptic problems with critical Trudinger-Moser nonlinearities
Kanishka Perera, Inbo Sim
We prove the existence of a positive solution to a semipositone -Laplacian problem with a critical Trudinger-Moser nonlinearity. The proof is based on obtaining uniform $C^{1,α}…
Existence results for Schrödinger -Laplace equations involving critical growth in
Ky Ho, Yun-Ho Kim, Inbo Sim
We establish some existence results for Schrödinger -Laplace equations in with various potentials and critical growth of nonlinearity that may occur on some no…
A note on fractional -Laplacian problems with singular weights
Ky Ho, Kanishka Perera, Inbo Sim +1
We study a class of fractional -Laplacian problems with weights which are possibly singular on the boundary of the domain. We provide existence and multiplicity results as well…