Existence Of Multiple Solutions For Two Class Of Nonlocal Problems With Singular Terms

In this paper,we study the existence of multiple solutions for two class of nonlocal problems with singular terms.Using the variational methods,the nonsmooth functional critical point theory and the Nehari manifolds,the existence of multiple solutions for two class of singular nonlocal problems is obtained.In the first class,we study the following nonlocal problems with logarithmic and singular terms (?)where ?(?)R~3 is a bounded domain with a smooth boundary,a,b>0,00 is a real parameter.By using the variational method and the critical point theory for non-smooth functional,the existence of multiple nontrivial solutions of the problem(0.3)are obtained.In the second class,we consider the solvability of the following nonlocal problems with critical and singular growth (?) where a,b>0,00 is a real parameter,f(x) and Q(x) is a positive continuous function on R~4.By the variational method and the Nehari method,we obtain that the problem(0.4)has the existence of multiple positive solutions.