Algorithm 90. A procedure realizing a second order one-step method solving a system of ordinary differential equations
The maximal operator S⁎ for the spherical summation operator (or disc multiplier) associated with the Jacobi transform through the defining relation for a function f on ℝ is shown to be bounded from into for (4α + 4)/(2α + 3) < p ≤ 2. Moreover S⁎ is bounded from into . In particular converges almost everywhere towards f, for , whenever (4α + 4)/(2α + 3) < p ≤ 2.
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.
We shall be concerned with the existence of almost homoclinic solutions for a class of second order functional differential equations of mixed type: , where t ∈ ℝ, q ∈ ℝⁿ and T>0 is a fixed positive number. By an almost homoclinic solution (to 0) we mean one that joins 0 to itself and q ≡ 0 may not be a stationary point. We assume that V and u are T-periodic with respect to the time variable, V is C¹-smooth and u is continuous. Moreover, f is non-zero, bounded, continuous and square-integrable....