Critical points and nonlinear variational problems
We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
We sharpen some previous results of [2, 4], dealing with a bifurcation problem arising in fluid dynamics.
We show that a class of semilinear boundary value problems possess exactly one positive solution and one negative solution.
Consider the variational, non-linear boundary value problem in a bounded open set . If and satisfy suitable conditions (see § 1), we prove that (1) has an infinite number of solutions, which are the critical points of a functional on a suitable manifold. This critical points are studied by means of Lusternik-Schnirelman theory.
The existence of solutions with prescribed period for a class of Hamiltonian systems with a Keplerian singularity is discussed.
The existence of solutions with prescribed period for a class of Hamiltonian systems with a Keplerian singularity is discussed.
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