Nontrival And Multiple Solutions For Elliptic Equations With Critical Exponents

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^{∞}(R^N) 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 R^N 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(R^N,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.