Global well-posedness and stability of constant equilibria in parabolic–elliptic chemotaxis
systems without gradient sensing Page 1 Nonlinearity PAPER Global well-posedness and …

Here we study the interaction and the configuration of spikes in a double condensate by
analyzing least energy solutions of two coupled nonlinear Schrödinger equations which …

We study the semiclassical limit for the following system of Maxwell--Schrödinger equations: -
ℏ^22mΔv+v+ωϕv-γv^p=0,\;\;-Δϕ=4πωv^2, where ℏ, m, ω, γ>0, v, ϕ:R^3→R, 1<p<117. This …

We exhibit new concentration phenomena for the equation− ε2 Δu+ u= up in a smooth
bounded domain Ω⊆ ℝ2 and with Neumann boundary conditions. The exponent p is …

We consider the following singularly perturbed Neumann problem: ϵ^ 2 Δ u-u+ f (u)=
0\enspace\rm in\Omega,\quad\it u>\rm 0\enspace\rm in\Omega, ∂\it u ∂ ν= 0\enspace\rm …

We study the equation− ε2Δu+ V (| x|) u= up, with ε> 0 and p> 1, in balls or annuli of ℝn,
under Neumann or Dirichlet boundary conditions. As ε tends to zero we prove existence of …

We continue the study of 34, proving concentration phenomena for the equation− ε 2 Δ u+
u= up in a smooth bounded domain Ω⊆ R^n and with Neumann boundary conditions. The …

Qualitative properties of solutions to elliptic equations can be interpreted in an extremely
broad sense to include virtually every property of solutions. In this chapter, however, I shall …

We study the following system of Maxwell-Schrödinger equations Δ uu-δ u\psi+ f (u)=
0,\quad Δ ψ+ u^ 2= 0 in\mathbb R^ N, u,\; ψ> 0,\quad u,\; ψ → 0\mbox as ‖ x| →+ ∞, where …

Let BR be a ball of radius R in R N. We analyze the positive solutions to the problem {− Δ u+
u=| u| p− 2 u, in BR,∂ ν u= 0, on∂ BR, that branch out from the constant solution u= 1 as p …