Existence Of Multiple Weak Solutions For Two Kinds Of Nonlocal Problems

In this paper,by using the variational method,Nehari manifold and some analysis techniques,we study the existence and multiplicity of weak solutions for two kinds of nonlocal problems.Firstly,we consider the following nonlocal problem with Sobolev critical exponents and concave terms where a,b?>0,1<q<2,g?L4/4-q(R4)is a contionuous function that is almost everywhere greater than zero.We obtain the existence and multiplicity of positive solutions for problem(0.1)via the Mountain Pass Lemma and Ekeland's variational principle.Secondly,we consider the following nonlocal problem with Hardy-Sobolev critical exponents and singular terms where a,b>0,0<?<1,0?k<1/4,0?s<2,?>0 are real parameters,0(?)f? L?(R3),there is Q>0 such that suppf(?)B,(0)?The existence of multiple positive solutions of equation(0.2)is obtained by using Nehari manifold and Ekeland's variational principle.