Sign-changing blowing-up solutions for supercritical Bahri–Coron’s problem

Sign-changing Blowing-up Solutions for Supercritical Bahri-coron’s Problem

Let Ω be a bounded domain in Rn, n ≥ 3 with smooth boundary ∂Ω and a small hole. We give the first example of sign-changing bubbling solutions to the nonlinear elliptic problem −∆u = |u| n+2 n−2+ε−1u in Ω, u = 0 on ∂Ω, where ε is a small positive parameter. The basic cell in the construction is the signchanging nodal solution to the critical Yamabe problem −∆w = |w| 4 n−2w, w ∈ D(R) which has l...

Sign-changing Blow-up Solutions for Yamabe Problem

Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. We are concerned with the following elliptic problem ∆gu+ hu = |u| 4 n−2−εu, in M, where ∆g = −divg(∇) is the Laplace-Beltrami operator on M , h is a C1 function on M , ε is a small real parameter such that ε goes to 0.

Blowing up solutions for an elliptic Neumann problem with sub - or supercritical nonlinearity Part I : N 1⁄4 3

We consider the subor supercritical Neumann elliptic problem Du þ mu 1⁄4 u5þe; u40 in O; @u @n 1⁄4 0 on @O; O being a smooth bounded domain in R ; m40 and ea0 a small number. Hm denoting the regular part of the Green’s function of the operator Dþ m in O with Neumann boundary conditions, and jmðxÞ 1⁄4 m 1 2 þ Hmðx; xÞ; we show that a nontrivial relative homology between the level sets jm and j b...

Infinitely many solutions for a bi-nonlocal‎ ‎equation with sign-changing weight functions

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.

Asymptotic and Numerical Results for Blowing - Up Solutions