## Topological Methods in Nonlinear Analysis

### Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces

#### Abstract

An existence result for an abstract 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 48, Number 2 (2016), 613-636.

Dates
First available in Project Euclid: 21 December 2016

https://projecteuclid.org/euclid.tmna/1482289232

Digital Object Identifier
doi:10.12775/TMNA.2016.061

Mathematical Reviews number (MathSciNet)
MR3642776

Zentralblatt MATH identifier
1365.34106

#### Citation

Benedetti, Irene; Väth, Martin. Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces. Topol. Methods Nonlinear Anal. 48 (2016), no. 2, 613--636. doi:10.12775/TMNA.2016.061. https://projecteuclid.org/euclid.tmna/1482289232

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