Positive Solutions For Singular Elliptic Equations In Different Boundary Conditions

This dissertation collects the main results obtained by the author during the period when he has worked for the M.D. The contents are as the fallowings:Firstly, we study the existence of nontrivial solution for the following quasilinear elliptic equationsA detailed analysis on the (PS) sequence of the variational functionals corresponding to the equations is given and a local compactness result is obtained. By choosing special Mountain Pass theorem and energy estimate, we obtain if the variational functionals corresponding to the equations satisfy local (PS) condition, there exsit a critical point, then we prove the exitence of positive solutions.In chapter two, we study the existence of positive solution for the following elliptic equations in the condition ofIt is different from 0∈Ω. We prove the variational functional corresponding to the equation(2) satisfy local (PS) condition, and obtain a general exitence theorem, then applying the theorem and energy estimate, obtain the exitence of positive solutions.