An Indirect Method of Nonconvex Variational Problems in Asplund Spaces: The Case for Saturated Measure Spaces

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The purpose of this paper is to establish an existence result for nonconvex variational problems with Bochner integral constraints in separable Asplund spaces via the Euler--Lagrange inclusion, under the saturation hypothesis on measure spaces, which makes the Lyapunov convexity theorem valid in Banach spaces. The approach is based on the indirect method of the calculus of variations.

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