Ntouyas, S. K.; Tsamatos, P. Ch. Global existence for semilinear evolution equations with nonlocal conditions. (English) Zbl 0884.34069 J. Math. Anal. Appl. 210, No. 2, 679-687 (1997). The authors apply Schauder’s fixed-point theory to differential equations in Banach spaces, \[ x'(t)= Ax(t)+ f(t,x(t)) \] with nonlocal initial conditions of the type \[ x(0)+ g(x)= x_0. \] Here, \(t\in[0, b]\), and some general assumptions on \(g: C([0,b], X)\to X\) and \(f:[0, b]\times X\to X\) are given which guarantee the existence of a solution \(x\in C([0,b], X)\). Reviewer: R.Illner (Victoria) Cited in 1 ReviewCited in 95 Documents MSC: 34G20 Nonlinear differential equations in abstract spaces 34K30 Functional-differential equations in abstract spaces Keywords:differential equations in Banach spaces; initial conditions PDF BibTeX XML Cite \textit{S. K. Ntouyas} and \textit{P. Ch. Tsamatos}, J. Math. Anal. Appl. 210, No. 2, 679--687 (1997; Zbl 0884.34069) Full Text: DOI OpenURL