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

0468423 - MÚ 2017 RIV PL eng J - Journal Article
Benedetti, I. - Väth, Martin
Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces.
Topological Methods in Nonlinear Analysis. Roč. 48, č. 2 (2016), s. 613-636. ISSN 1230-3429. E-ISSN 1230-3429
Institutional support: RVO:67985840
Keywords : weak measure of noncompactness * weakly condensing map * semilinear differential inclusion
Subject RIV: BA - General Mathematics
Impact factor: 0.667, year: 2016
http://www.apcz.pl/czasopisma/index.php/TMNA/article/view/TMNA.2016.061

An existence result for an abstract nonlocal boundary value problem $x'in A(t)x(t)+F(t,x(t))$, $Lxin B(x)$, 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.
Permanent Link: http://hdl.handle.net/11104/0266281