Esmaeil Yousefi - Karaj Islamic Azad University, Iran, Karaj
Daryoush Kalvand - Karaj Islamic Azad University, Iran, Karaj

We consider the mixed problem for the equation Lu = (t u)+  Au = f ,where a linear A operator acting in a separable Hilbert space H has a complete system of eigenfunctions, which form a Riesz basis in H . We investigate the question of the existence and uniqueness of generalized solutions of the mixed problem for the equation (1), as well as give a description of the spectrum for the corresponding operator.

Mixed problem, weighted Sobolev spaces, differential equations in abstract