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On the solutions of nonlinear initial-boundary value problems. (English) Zbl 1063.35017

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.

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.)
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