Bessel (Riesz) potentials on Banach function spaces and their applications II, on existence of solutions for a class of nonlinear evolution equations

摘要

First, we apply the main results in [19] to the study for a class of nonlinear integral equations, the existence of solutions in H-s (0 < s < infinity) for these equations is shown. Next, as some applications, we get the local existence of solutions in H-s for a class of nonlinear (higher order) Schrodinger equations. Moreover, in some additional conditions these solutions axe global. Finally, the existence of H-s-solutions for Ginzburg-Landau equations and for nonlinear higher order wave equations is obtained. [References: 19]