### Sets of solutions of nonlinear initial-boundary value problems

DOI: http://dx.doi.org/10.12775/TMNA.2001.011

#### 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.

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.

#### Keywords

Initial-boundary value problem; Fredholm operator; Hölder space; bifurcation point; surjectivity

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