Sign-changing solutions to elliptic second order equations: glueing a   peak to a degenerate critical manifold
  We construct blowing-up sign-changing solutions to some nonlinear critical equations by glueing a standard bubble to a degenerate function. We develop a method based on analyticity to perform the glueing when the critical manifold of solutions is degenerate and no Bianchi--Egnell type condition holds. 
Fr\'ed\'eric Robert and J\'er\^ome V\'etois
math.AP