Sets of solutions of nonlinear initial-boundary value problems
KeywordsInitial-boundary value problem, Fredholm operator, Hölder space, bifurcation point, surjectivity
AbstractIn 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.
How to Cite
ĎURIKOVIČ, Vladimír & ĎURIKOVIČOVÁ, Monika. Sets of solutions of nonlinear initial-boundary value problems. Topological Methods in Nonlinear Analysis [online]. 1 March 2001, T. 17, nr 1, s. 157–182. [accessed 28.3.2023].
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