Bifurcation from infinity in a nonlinear elliptic equation involving the limiting Sobolev exponent

International audienceWe consider an elliptic PDE with critical nonlinearity, and additonal subcritical and super quadratic nonlinearity, with Dirichlet boundary conditions, on a 3-dimensional smooth and bounded domain. We prove the existence of at least p+1 solutions, where p is the Ljusternik-Schnirelman category of the domain. We prove additional results concerning double peaked solutions on a ringshaped domain. In particular, we characterize the points at which the solutions blow up as the ringshaped domain becomes thinner or thicker