Sets of solutions of nonlinear initial-boundary value problems

Abstract

In this paper 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 Nemitskiĭ 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 for the different mechanical and natural science models.