Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces
Keywords
Weak measure of noncompactness, weakly condensing map, semilinear differential inclusion, nonlocal boundary condition, fixed point theorems with weak topology, containment resultAbstract
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.References
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