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Existence results for semilinear differential equations with nonlocal and impulsive conditions. (English) Zbl 1193.35099

The authors consider the following impulsive differential equation with nonlocal conditions:

u ' (t)=Au(t)+f(t,u(t)),0tb,tt i ,u(0)=g(u),Δu(t i )=I i (u(t i )),i=1,2,,p,0<t i <<t p <b,

where A is the infinitesimal generator of a C 0 -semigroup on a real Banach space X and f, g, I i are appropriate continuous functions.

Existence results are obtained for mild solutions without the compactness or Lipschitz continuity assumptions on impulsive functions. Two examples are given to illustrate the results.

35K58Semilinear parabolic equations
47D06One-parameter semigroups and linear evolution equations
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