TY - JOUR AU - I. Ya. Kmit PY - 2013/03/25 Y2 - 2024/03/29 TI - Fredholm solvability of a periodic Neumann problem for a linear telegraph equation JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 3 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2425 AB - We investigate a periodic problem for the linear telegraph equation$$u_{tt} - u_{xx} + 2\mu u_t = f (x, t)$$with Neumann boundary conditions. We prove that the operator of the problem is modeled by a Fredholm operator of index zero in the scale of Sobolev spaces of periodic functions. This result is stable under small perturbations of the equation where p becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions of this problem possess smoothing properties. ER -