GROUND STATE SOLUTION OF A NONLOCAL BOUNDARY-VALUE PROBLEM

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation -(a+b integral(Omega) vertical bar del u vertical bar(2)dx)Delta u = f(x, u) subject to Dirichlet boundary conditions. Under a general 4-superlinear condition on the nonlinearity f, we prove the existence of a ground state solution, that is a nontrivial solution which has least energy a mong the set of nontrivial solutions. If f is odd with respect to the second variable,we also obtain the existence of infinitely many solutions. Under our assumptions the Nehari manifold does not need to be of class C-1.