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VIABILITY FOR A CLASS OF PARTIAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NON-DENSE DOMAIN
  • YASSIN STAILI,
  • Khalil Ezzinbi
YASSIN STAILI
Universite Cadi Ayyad Faculte des Sciences Semlalia

Corresponding Author:[email protected]

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Khalil Ezzinbi
Universite Cadi Ayyad Faculte des Sciences Semlalia
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Abstract

Let E be a Banach space, A:D(A)⊂E→E be a linear operator on E. Denote by D a locally closed subset of E and F:[0,+∞)×B→E a continuous function. A sufficient condition for D to be a forward invariant set of the following partial functional differential equation with infinite delay dv(t)/dt=Av(t)+F(t,vt),for t⩾0, v_0=ϕ∈B, is the tangency condition namely: there exists a bounded linear operator B:D(A) ̄→E such that for every ξ>0 and τ>0 there exists γ>0 such that: lim_h→0^+ (1/h)d(T(A−γB)_0(h)ϕ(0)+S(A−γB)(h)[F(t,ϕ)+γBϕ(0)],D)=0, for every t∈[0,τ] and every ϕ∈B with ∥ϕ∥⩽ξ and ϕ(0)∈D.