6 papers
Uniqueness and multiplicity of positive radial solutions to the super-critical Brezis-Nirenberg problem in an annulus
Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe
The super-critical Brezis-Nirenberg problem in an annulus is considered. The new uniqueness result of positive radial solutions is established for the three-dimensional case. It is…
Uniqueness and multiple existence of positive radial solutions of the Brezis-Nirenberg Problem on annular domains in
Naoki Shioji, Satoshi Tanaka, Kohtaro Watanabe
The uniqueness and multiple existence of positive radial solutions to the Brezis-Nirenberg problem on a domain in the 3-dimensional unit sphere \begin{equation*} \l…
Rabinowitz alternative for non-cooperative elliptic systems on geodesic balls
Sławomir Rybicki, Naoki Shioji, Piotr Stefaniak
The purpose of this paper is to study properties of continua (closed connected sets) of nontrivial solutions of non-cooperative elliptic systems considered on geodesic balls in $S^…
Nonlocal problems at critical growth in contractible domains
Sunra Mosconi, Naoki Shioji, Marco Squassina
We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitab…
Coron problem for fractional equations
Simone Secchi, Naoki Shioji, Marco Squassina
We prove that the critical problem for the fractional Laplacian in an annular type domain admits a nontrivial solution provided that the inner hole is sufficiently small.
Symmetry of n-mode positive solutions for two-dimensional Hénon type systems
Naoki Shioji, Marco Squassina
We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply…