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

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)].

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

Citations:

Zbl 0915.34057
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