Existence And Multiplicity Of Solutions For Kirchhoff Type Problems

Kirchhoff type equation is a classical nonlocal problem,which has captured extensive interest in recent years.In this paper,we concern with the existence of solutions for two kinds of Kirchhoff type nonlinear elliptic equations with parameter.One of them has Dirichlet boundary conditions,and the other has nonlinear Neumann boundary condition.For the first equation,we study the existence and multiplicity of the solutions by using the variational principle when the parameter changes,and three results about existence of solutions are established.We also discuss the bifurcation of positive solutions for it.For the second equation,we use Bonanno and Bisci variational principle to study the existence of infinitely many solutions,and conditions that ensure the existence for infinitely many solutions are given.