Multiple Solutions Of A Singular Equation On Unbounded Domain Involving The P-Laplacian

In this thesis, we will be concerned with the following singular quasilinear elliptic equa-tion:whereΩ:= R~N\O, O is a bounded domain in R~N (N≥3),△_pu:= div(|(?)u|(p-2)(?)u) is p-Laplacian, 10isa real parameter,α,βare constants and 0 <α< 1, p <β+ 1 < p~*:= (?), f(x) and g(x) are continuous functions satisfying the following conditions:We note that the corresponding functional to (P_λ) fails to be Prechet differentiable, so the classical critical point theory cannot be used to solve this problem. In this thesis, by using the Ekeland variational principle combining the technique of the Nehari manifold decomposition, we obtain two positive (weak) solutions of Eq. (P_λ).