Global existence and stability of some semilinear problems. (English) Zbl 1048.34102

Kirane, M.; Tatar, N.-E.

Arch. Math., Brno 36, No. 1, 33-44 (2000).

Using a nonlinear singular version of the well-known Gronwall-Bellman inequality, the authors establish new existence and stability results for a semilinear parabolic equation and a semilinear functional-differential equation. These results improve results of M. Medved [Arch. Math., Brno 34, 183-190 (1998; Zbl 0915.34057)].

Reviewer: Aleksandr Lomtatidze (Brno)

MSC:

34K05	General theory of functional-differential equations
35B35	Stability in context of PDEs
35K55	Nonlinear parabolic equations
34K20	Stability theory of functional-differential equations

Keywords:

semilinear parabolic equation; functional-differential equation; integrodifferential equation; integral equation; fractional evolution equation; global existence; stability; variation of parameters

Citations:

Zbl 0915.34057