In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense...In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.展开更多
This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R...This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R(t,u). By using a generalized linking theorem for strongly indefinite functionals, we prove the existence of homoclinic orbits for both the super-quadratic case and the asymptotically linear one.展开更多
文摘In this paper we examine single-step iterative methods for the solution of the nonlinear algebraic equation f (x) = x2 - N = 0 , for some integer N, generating rational approximations p/q that are optimal in the sense of Pell’s equation p2 - Nq2 = k for some integer k, converging either alternatingly or oppositely.
基金supported by the Scientific Research Foundation of Graduate School of Southeast University, China (Grant No. YBJJ0928)
文摘This paper is concerned with the existence of homoclinic orbits for the second-order Hamiltonian system with obstacle item, ü(t)-A u(t) =▽F (t, u), where F (t, u) is T-periodic in t with ▽F (t, u) = L(t)u + ▽R(t,u). By using a generalized linking theorem for strongly indefinite functionals, we prove the existence of homoclinic orbits for both the super-quadratic case and the asymptotically linear one.
