Abstract and Applied Analysis
Volume 2004 (2004), Issue 5, Pages 407-424

On the solutions of nonlinear initial-boundary value problems

Vladimír Ďurikovič1 and Monika Ďurikovičová2

1Department of Applied Mathematics, SS. Cyril and Methodius University, nám. J. Herdu 2, Trnava 917 00, Slovakia
2Department of Mathematics, Slovak Technical University, nám. Slobody 17, Bratislava 812 31, Slovakia

Received 27 September 2002

Copyright © 2004 Vladimír Ďurikovič and Monika Ďurikovičová. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 operatortheory. 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.