Solutions of prescribed number of zeroes to a class of superlinear ODE's systems

Abstract

We consider a class of superlinear conservative ordinary differential systems in Newtonian form:¶ $ -\ddot U=\nabla E(t,U),\qquad U(t)\in \Bbb R^n $ ¶ with $ t\in[A,B] $ . We prove the existence of infinitely many solutions to the Dirichlet boundary value problem. Such solutions are characterized by the number of zeroes of each component. Our argument is based upon an extension of the Nehari variational method [11].