Existence Of Solutions For A Class Of Quasilinear Elliptic Equations With Weights

In this thesis, we study the existence of solutions of following quasilinear elliptic equationwhereΩis a bounded domain with smooth boundary in R~N(N≥3) a,b are nonnegative function onΩ,f_λare given function under the certain assumptions.λ> 0,μ> 0.The thesis consists of four chapters.In chapter one, we recall some background and results on the existence of problem (P_λ) .In chapter two, we introduce some basic knowledge of critical point theory, and give some notations and Lemma.In chapter three, we study the following elliptic equation with singularitywhere 0∈Ωis a bounded domain with smooth boundary in R~N(N≥3) ,λ> 0, 0≤μ<μ= (N-2- 2α)~2/4, -∞<α<(N - 2)/2, hereμis the best constant in the Caffarelli-Kohn-Nirenberg(ef.[17, Theorem 1.1]) :we obtain the existence of solutions of problem (P_λ) by using of Mountain Pass Theorem and the translation method.In chapter four, we study the following degenerate equationwhere a is a nonnegative function onΩ,λ> 0 is a real parameter, 1 < q < 2, f, g are given function under the certain assumptions . we obtain the existence of solutions of problem (P_λ) by using of Mountain Pass Theorem .