| We deal with some elliptic equations with critical exponents in this dissertation. In the second chapter, we consider the following quasilinear elliptic equationwhere a, fi are real parameters, , h{x) € L∞(RN) and h(x) ≥ h0 >0. We prove that under certain conditions problem (1) has multiple solutions.In the third chapter, we intend to study the multiplicity of solutions for the following singular elliptic equation with Hardy- Sobolev exponentwhere Ω is a bounded domain in RN with smooth boundary. The concentration compactness principle is used to prove that the Palais-Smale condition is satisfied below a certain level.In the fourth chapter, we study the existence and the concentration behavior of ground state for the equationwhere ε, λ> 0, 1 < p < N, and V(x) ∈ C1(RN,R) satisfies the condition such that . In addition to the certain hypotheses, for any T > 0we conclude that the corresponding Schrodinger equation to (3)has a standing wave solution with time period T. |
