Multivalued evolution equations with nonlocal initial conditions in Banach spaces

Article

DOI: 10.1007/s00030-007-5049-5

Cite this article as:
Aizicovici, S. & Staicu, V. Nonlinear differ. equ. appl. (2007) 14: 361. doi:10.1007/s00030-007-5049-5

Abstract.

We prove the existence of integral solutions to the nonlocal Cauchy problem \(u{\prime}(t)\epsilon-Au(t)+F(t,u(t)), 0{\leq}\,t\, {\leq}\,T; u(0)=g(u)\) in a Banach space X, where \(A : D\,(A)\, {\subset}\, X \rightarrow X\) is m-accretive and such that –A generates a compact semigroup, \(F : [0,T] \times X \rightarrow 2^{X}\) has nonempty, closed and convex values, and is strongly-weakly upper semicontinuous with respect to its second variable, and \(g :C \left([0,T]; \overline{D\,(A)}\right) \rightarrow \overline{D\,(A)}\). The case when A depends on time is also considered.

2000 Mathematics Subject Classification:

34G25 35K90 47J35 

Keywords:

Nonlocal Cauchy problem evolution inclusion m-accretive operator compact semigroup multifunction 
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Copyright information

© Birkhaueser 2007

Authors and Affiliations

  1. 1.Department of MathematicsOhio UniversityAthensUSA
  2. 2.Department of MathematicsAveiro UniversityAveiroPortugal

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