In this thesis, we will work around the eigenvalue problem 8< : 􀀀 pu = jujp􀀀2u in u = 0 on @ where p is the p- Laplacian operator, with 1 < p < 1, which is a generalization of the Laplacian operator (p = 2) ...

The study of existence, multiplicity and non-existence of positive solutions to semi-linear and quasi-linear elliptic equations is relevant to many applications ranging from thermal iginition of gases [14], quantum field ...