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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.

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