  We study the $J-$holomorphic curves in the symplectization of the contact
manifolds and prove that there exists at least one periodic Reeb orbits in any
closed contact manifold with any contact form by using the well-known Gromov's
nonlinear Fredholm alternative for $J-$holomorphic curves. As a corollary, we
give a complete solution on the well-known Weinstein conjecture.
