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

Irene Benedetti, Martin Väth


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.


Weak measure of noncompactness; weakly condensing map; semilinear differential inclusion; nonlocal boundary condition; fixed point theorems with weak topology; containment result

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