Some Variational Problems Without Compactness

In this dissertation we consider some nonlinear elliptic equations. The common point of these equations is the variational functionals corresponding to them do not satisfy Palais-Smale condition.In the first, we study a nonlinear Schrodinger equation. We give general conditions which assure the existence of ground state solutions. Under a Nehari type condition, we show that the standard Ambrosetti-Rabinowitz super-linear condition can be replaced by a more natural super-quadratic condition.Then the next chapter is concerned with the existence of infinitely many solutions of the elliptic equation with indefinite weight. The indefinite weight is afunction possibly changing sign in R~N.Finally we devoted to the existence of infinitely many solutions of the p-Laplacian elliptic equation, considered the case of p ≠ 2 in the Δ_p operator. Our goal is to find the existence of infinitely many radial and non-radial solutions of the equation.