Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces
- 1 June 2016
- journal article
- Published by Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University in Topological Methods in Nonlinear Analysis
- Vol. 48 (1), 1
- https://doi.org/10.12775/TMNA.2016.061
Abstract
An existence result for an nonlocal boundary value problem $x'\in A(t)x(t)+F(t,x(t))$, $Lx\in B(x)$, is given, where $A(t)$ determines a linear evolution operator, $L$ is linear, and $F$ and $B$ are multivalued. To avoid compactness conditions, the weak topology is employed. The result applies also in nonreflexive spaces under a hypothesis concerning the De Blasi measure of noncompactness. Even in the case of initial value problems, the required condition is essentially milder than previously known results.