Construction of singular limits for a semilinear elliptic equation in dimension 2

Multiple Condensations for a Nonlinear Elliptic Equation With Sub-Critical Growth and Critical Behaviour

“…Remark 1.8. We remark that our results here in some sense are a generalization of those in [5]. In [5], Baraket and Pacard considered the following problem:…”

Convergence for a Liouville equation

“…The problem (1.1-2) also has other interesting features, which are different from other nonlinear problems like Nirenberg's problem (see [15]) and the scalar curvature problem (see [2]); in particular the blow-up analysis of H.Brezis and F.Merle [3]. In fact, for (1.1-2) we do have multiple bubbles [12] and when K = 1 , S.Baraket and F.Pacard [26] construct them by using the fixed point theorem. By contrast, we point out that there is at most one bubble for a Palais-Smale sequence in Nirenberg's problem.…”

Singular Limits of a Two-Dimensional Boundary Value Problem Arising in Corrosion Modelling

“…It follows from those results that concentration occurs in the form λe u 8π δ ξj . In [1,5,6] solutions with these properties have been built. In [3] the problem (1.6) ∆u − u = 0, ∂u ∂ν = λe u was analyzed and given any k ≥ 1, a solution peaking in such a way that λe u 4π k j=1 δ ξj was built up, using as basic cells (after suitable zoomingup) explicit solutions of…”