On Biharmonic Equations Involving Critical Exponent

In the papers, We discuss some biharmonic equations with critical exponents.Firstly, we deals with the existence of a weak solutions for the following bihar-monic equation with double critical exponents: where Dn2,2(RN) is the closure of C0∞(RN) functions with respect to the norm [|u||= (?),associated with inner product given by (u, v) =(?),2**(s)= (?),0< s< N,2**=(?) is the critical Sobolev exponent for the embedding W2,2(RN)→L2/**/ (RN).we are interested in the existence of nontrivial weak solu-tions of(BCB).Then,we study the following baiharmonic problem with critical exponent: (?), in RN, (BD) whereλ> 0 is a parameter,0≤q< 2*=(?),h(x)is both nonnegative and integrable on RN, H is the Heaviside function.Using variational arguments and analysis techniques,we establish the existence of the nontrivial solutions in the disguishing cases:0≤q≤1;1<q<2**...