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. 
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     author = {I. G. Tsar'kov},
     title = {Approximative compactness and nonuniqueness in variational problems, and applications to differential equations},
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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/