Topological Methods in Nonlinear Analysis

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

Irene Benedetti and Martin Väth

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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

Permanent link to this document
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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