Bekkouche, Noria2014-11-182014-11-182014-11-18https://dspace.univ-tlemcen.dz/handle/112/6830Par la méthode variationnelle nous montrons l’existence et la multiplicitéde solutions non radiales pour le problème (I). On distinguera deux cas....We study the following elliptic problem : (I) ( ) ( ) ( ) ( ) ( ) , 0 u x g x u x f x x u x x  −∆ = + ∈ Ω   = ∈ ∂Ω   Were Ω is the unit ball in n R ( ) 2 n ≥ , and ( ) 2 f L ∈ Ω and g is acontinuous, odd and sublinear function. By the variational method we obtain the existence of infinity non radial solution to (I).we distinguish two cases.frproblème elliptique, minimisationavec contraintes, la condition de plais smale, théorème du col, solution périodiqueproblem elliptics, minimization with contraints, the palais smalecondition, mountain pass théorem, periodic solution.Thesis