Abstract and Applied Analysis
Volume 2004 (2004), Issue 5, Pages 407-424
doi:10.1155/S1085337504306081
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
Abstract
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.