Geodesic
Approximative compactness and nonuniqueness in variational problems, and applications to differential equations
Sbornik. Mathematics, Tome 202 (2011) no. 6, pp. 909-934

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The paper is concerned with the study of sets which are approximatively compact with respect to a family of functionals obtained by subtracting affine functionals from some fixed base functional. Nonconvexity of the base functional is shown to imply the minimum in a variational problem with some modified functional is not unique. The results obtained are applied to a specific equation involving the $q$-Laplacian. Bibliography: 7 titles.
Keywords: approximative compactness, variational problem, nonlinear differential equation. 
I. G. Tsar'kov. Approximative compactness and nonuniqueness in variational problems, and applications to differential equations. Sbornik. Mathematics, Tome 202 (2011) no. 6, pp. 909-934. http://geodesic.mathdoc.fr/item/SM_2011_202_6_a5/
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