Extrema of nonlocal functionals and boundary value problems for functional differential equations (Q2784707)

The paper deals with a nonlocal integral functional whose integrand is a two-variable function such that: it depends on the derivative with respect to the first variable, whereas the shift operator is applied with respect to the second one. NEWLINENEWLINENEWLINEA necessary condition for weak extrema in terms of a generalized Euler equation was proved in [\textit{G. A. Kamenskij}, Nonlinear Anal. Theory Methods Appl. 18, 801-813 (1992; Zbl 0787.34054)]. In the present paper the authors provide a sufficient condition for weak local extrema satisfying certain boundary value conditions.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].