On the solutions of nonlinear initial-boundary value problems

Abstract

We deal with the general initial-boundary value problem for a second-order nonlinear nonstationary evolution equation. The associated operator equation is studied by the Fredholm and Nemitskii operator theory. Under local Hölder conditions for the nonlinear member, we observe quantitative and qualitative properties of the set of solutions of the given problem. These results can be applied to different mechanical and natural science models.