Nonresonance problems

for differential inclusions

in separable Banach spaces

Authors:
Zouhua Ding and Athanassios G. Kartsatos

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2357-2365

MSC (1991):
Primary 34A60

DOI:
https://doi.org/10.1090/S0002-9939-96-03439-9

MathSciNet review:
1340383

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a real separable Banach space. The boundary value problem

is studied on the infinite interval Here, the closed and densely defined linear operator generates an evolution operator The function is measurable in its first variable, upper semicontinuous in its second and has weakly compact and convex values. Either is bounded and is compact for or is compact and is equicontinuous. The mapping is a bounded linear operator and is fixed. The nonresonance problem is solved by using Ma's fixed point theorem along with a recent result of Przeradzki which characterizes the compact sets in

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Additional Information

**Zouhua Ding**

Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700

Email:
ding@chuma.usf.edu

**Athanassios G. Kartsatos**

Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700

Email:
hermes@gauss.math.usf.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03439-9

Keywords:
Boundary value problem on an infinite interval,
differential inclusion,
upper semicontinuous function,
compact evolution operator

Received by editor(s):
December 16, 1994

Communicated by:
Hal L. Smith

Article copyright:
© Copyright 1996
American Mathematical Society