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The nonlinearities are dominated by a triangular form satisfying linear growth condition in the unmeasurable states with an unknown growth rate.
In this paper, we consider a Carathéodory map f satisfying a growth condition different from (1.5).
In addition, is a given function satisfying the growth condition (2.6).
Clearly, the mapping is a Carathéodory function satisfying the growth condition (3.16).
For satisfying the growth condition for some positive integer as, we obviously have (3.20).
The right-hand side is a Carathéodory function satisfying a growth condition of Wintner-Nagumo type.
In these papers, the nonlinearity is again satisfying suitable growth conditions at and.
Lemma 3.4Let ξ 0 ∈ ∧ l 1 × ⋯ × ∧ l m andWbe quasiconvex satisfying the growth condition (1.1).
Conversely, every -solution of the heat equation satisfying the growth condition (4.11) can be uniquely expressed as for some.
In this paper, we consider the existence of a random attractor for (1.1 - 1.3 1.1 - 1.3erior forcing term g ( x, u ) satisfying some growithconditions.
where Ω is a bounded C1 domain in R n and f : R n × R m × R nm → R is a Caratheodory function satisfying variable growth conditions.
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