Solutions For A Class Of Elliptic Equations

We will focus on some problems for the existence and non-existence of solutons for a class of nonlinear elliptic equations.In chapter one, We deal with existence, non-existence of solutions of the following elliptic problemwhereΩ(?) R^N is a bounded domain with smooth boundary (?)Ω.In chapter two, we prove the existence of n₁ -n₂ pairs of nontrivial solutions for the elliptic equation of high orderwhere m≥2, n₁ > n₂, m, n₁ and n₂ arc all integers.