We consider the following slightly supercritical problem for the Lane-Emden system with
Neumann boundary conditions:\begin {equation*}\begin {cases}-\Delta u_1 …

Abstract We consider the Lane-Emden system {− Δ u= vp in Ω,− Δ v= uq in Ω, u, v> 0 in Ω, u=
v= 0 on∂ Ω where Ω is a smooth bounded domain in R n for n≥ 3 and 0< p< q<∞. The …

Despite its simple form, this problem has been an amazing source of open problems, and
the process of understanding it has helped develop new and interesting techniques which …

We consider the following supercritical problem for the Lane-Emden system:\begin
{equation}\label {eq00}\begin {cases}-\Delta u_1=| u_2|^{p-1} u_2\&in\D,\\-\Delta u_2 …

We consider the following slightly subcritical problem (℘ ε){− Δ u= β (x)| u| p− 1− ε u in Ω, u=
0 on∂ Ω, where Ω is a smooth bounded domain in R n, 3≤ n≤ 6, p:= n+ 2 n− 2 is the …

INFINITELY MANY POSITIVE SOLUTIONS FOR AN NONLINEAR FIELD EQUATION WITH
SUPER-CRITICAL GROWTH 1. Introduction In this paper, we Page 1 INFINITELY MANY …

We consider the problem-Δ u=| u|^ p-2 u\;\; in\; Ω,\quad u= 0\; on\; ∂ Ω where Ω:=\left {(y, z)
∈ R^ m+ 1 * R^ Nm-1: 0< a<| y|< b< ∞\right\}, 0 ≦ m ≦ N-1\; and\; N ≧ 2.\; Let\; 2^* _ N, m …

We exhibit a new concentration phenomenon for the supercritical problem-Δ⁢ v= λ⁢ v+| v| p-
2⁢ v in⁢ Ω, v= 0 on⁢∂⁡ Ω, as p→ 2 N, m∗ from below, where 2 N, m∗:= 2⁢(Nm) Nm-2, 1≤ …

We consider the supercritical problem− Δ u=| u| p− 1 u in D, u= 0 on∂ D, where D is a
bounded smooth domain in RN and p is smaller than the κ-th critical Sobolev exponent 2 N …

In this article, we study the following Hamiltonian elliptic system with coefficients: $\begin
{align}\notag\left\{\begin {aligned}-\varepsilon^ 2\Delta u+ c (x) u= b (x)|{v}|^{q-1} v …