Sets of solutions of nonlinear initial-boundary value problems

Vladimír Ďurikovič, Monika Ďurikovičová

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.

Keywords


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

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