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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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