×

zbMATH — the first resource for mathematics

Global existence for semilinear evolution equations with nonlocal conditions. (English) Zbl 0884.34069
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 \(x\in C([0,b], X)\).

MSC:
34G20 Nonlinear differential equations in abstract spaces
34K30 Functional-differential equations in abstract spaces
PDF BibTeX XML Cite
Full Text: DOI