Ground state solution of a nonlocal boundary-value problem

الأصل · EN

In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation equation* -(a+b∫Ω|∇ u|²dx)Δu=f(x,u) equation* submitted 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 among the set of nontrivial solutions. In case which 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 C¹.