Singular limits for the bi-Laplacian operator with exponential nonlinearity in $\mathbb R^{4}$

Abstract

Let Ω be a bounded smooth domain in R 4 such that for some integer d 1 its d-th singular cohomology group with coefficients in some field is not zero, then problemo n∂Ω, has a solution blowing-up, as ρ → 0, at m points of Ω, for any given number m.

Existence and multiplicity results for a fourth order mean field equation

“…See the works [2,7,10,12,11,[15][16][17]25,26] and references therein. Coming back to our fourth order mean field Eq.…”

Topological degree for solutions of fourth order mean field equations

“…There is now an extensive literature about this problem, we refer to Adimurthi et al [1], Baraket et al [3], Clapp et al [9], Druet and Robert [10], Hebey and Robert [11], Hebey et al [12], Malchiodi [20], Robert and Wei [24] and the references therein. In particular, we mention the two papers [3,9], where they constructed m-point blowing-up solutions for…”

“…In particular, we mention the two papers [3,9], where they constructed m-point blowing-up solutions for…”

“…under either nondegenerate conditions ( [3]) or topological nontrivial condition ( [9]). The organization of this paper is as follows: In Sect.…”

Gluing metrics with prescribed $Q$-curvature and different asymptotic behaviour in high dimension

“…with Dirichlet boundary conditions and the bound ρ k ≤ C, using the Lyapunov-Schmidt reduction, several results have been produced, both in dimension 2 (see e.g. [3,7,9]), 4 (see [2,6]) or higher (see [24]). In this case one can construct solutions blowing up at finitely many points, which are located at a critical point of a so-called reduced functional (compare to [26]).…”