Ďurikovič, Vladimír; Ďurikovičová, Monika On the solutions of nonlinear initial-boundary value problems. (English) Zbl 1063.35017 Abstr. Appl. Anal. 2004, No. 5, 407-424 (2004). Summary: 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 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 to different mechanical and natural science models. Cited in 1 Document MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 47F05 General theory of partial differential operators 47A53 (Semi-) Fredholm operators; index theories 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) Keywords:generic properties; nonparabolic models; Fredholm operator theory PDFBibTeX XMLCite \textit{V. Ďurikovič} and \textit{M. Ďurikovičová}, Abstr. Appl. Anal. 2004, No. 5, 407--424 (2004; Zbl 1063.35017) Full Text: DOI