We study singular radially symmetric solution of the stationary Keller-Segel equation, that is,
an elliptic equation with exponential nonlinearity, which is super-critical in dimension N≥ 3 …

In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion
system which models chemotaxis with local sensing. This system has the same gradient flow …

We investigate the behaviour of radial solutions to the Lin–Ni–Takagi problem in the ball
BR⊂ RN for N≥ 3:-▵ up+ up=| up| p-2 up in BR,∂ ν up= 0 on∂ BR, when p is close to the …

In this paper we consider the Liouville equation Δ u+ λ 2 eu= 0 with Dirichlet boundary
conditions in a two dimensional, doubly connected domain Ω. We show that there exists a …

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Given a smooth bounded domain $\Omega $ in $\mathbb {R}^ 2$, we study the following
anisotropic Neumann problem $$\begin {cases}-\nabla (a (x)\nabla u)+ a (x) u=\lambda a (x) …

We consider equations of the form∆ u+ λ2V (x) eu= ρ in various two dimensional settings.
We assume that V> 0 is a given function, λ> 0 is a small parameter and ρ= O (1) or ρ→+∞ as …

This thesis is devoted to the analysis of singularities in nonlinear elliptic partial differential
equations arising in mathematical physics, mathematical biology, and conformal geometry …