Asymptotic boundary value problems in Banach spaces

摘要: Abstract A continuation principle is given for solving boundary value problems on arbitrary (possibly infinite) intervals to Caratheodory differential inclusions in Banach spaces. For this aim, the appropriate fixed point index defined condensing decomposable multivalued operators Frechet This extends and unifies one compact maps Andres et al. [Trans. Amer. Math. Soc. 351 (1999) 4861–4903] as well spaces Bader [Ph.D. Thesis, University of Munich, 1995]. As an application, we prove existence entirely bounded solution a semilinear evolution inclusion.