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\(\Gamma\)-convergence for a class of functionals with deviating argument. (English) Zbl 0892.49006
The paper is concerned with functionals with deviating argument of the form \[ I(x)=\int_0^1 f\bigl(t,x(h_1(t)),\ldots,x(h_k(t)),\dot{x}(g_1(t)), \ldots,\dot{x}(g_l(t))\bigr) dt \] with the constraints \(x(t)=\dot{x}(t)=0\) for \(t\notin [-1,1]\). The trajectory \(x:{\mathbb{R}}\to{\mathbb{R}}^n\) is assumed to be absolutely continuous, and the problem of continuous dependence of the set of solutions on the data (i.e., \(f\), \(h_i\), \(g_j\)) is investigated using the theory of \(\Gamma\)-convergence.
Reviewer: L.Ambrosio (Pavia)

MSC:
49J45 Methods involving semicontinuity and convergence; relaxation
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