We investigate a steady planar flow of an ideal fluid in a bounded simply connected domain
and focus on the vortex patch problem with prescribed vorticity strength. There are two …

We concern a family $\{(u_ {\varepsilon}, v_ {\varepsilon})\} _ {\varepsilon> 0} $ of solutions
of the Lane-Emden system on a smooth bounded convex domain $\Omega $ in $\mathbb …

In this paper we consider steady vortex solutions for the ideal incompressible Euler equation
in a planar bounded domain. By solving a variational problem for the vorticity, we construct …

In this paper, we study the nearly critical Lane-Emden equations (⁎){− Δ u= up− ε in Ω, u> 0
in Ω, u= 0 on∂ Ω, where Ω⊂ RN with N≥ 3, p= N+ 2 N− 2 and ε> 0 is small. Our main result …

We compute the Morse index of 1-spike solutions of the semilinear elliptic problem (P p){− Δ
u= up in Ω u= 0 on∂ Ω u> 0 in Ω where Ω⊂ R 2 is a smooth bounded domain and p> 1 is …

We are concerned with the Lane-Emden problem {− Δ u= up in Ω, u> 0 in Ω, u= 0 on∂ Ω,
where Ω⊂ R 2 is a smooth bounded domain and p> 1 is sufficiently large. Improving some …

In this paper we are concerned with the well-known Brezis-Nirenberg problem\begin
{equation*}\begin {cases}-\Delta u= u^{\frac {N+ 2}{N-2}}+\varepsilon u, & {\text …

We obtain new sign changing solutions to the problem (℘∞)− Δ u=| u| 2⁎− 2 u, u∈ D 1, 2
(RN), for N≥ 4 where 2⁎:= 2 NN− 2 is the critical Sobolev exponent. These solutions arise …

Page 1 Cheſnctaxis, FEECtiºn, Netuurk Mathematics for Self-Organization - Takas hi Page 2
Cheſnotaxis, Reaction, NetLLDſk Mathematics for Self-Organization Page 3 This page …

We are motivated by the study of the Microcanonical Variational Principle within Onsager's
description of two-dimensional turbulence in the range of energies where the equivalence of …