Nonconvex variational problem with recursive integral functionals in Sobolev spaces: Existence and representation |
| |
Authors: | Nobusumi Sagara |
| |
Institution: | Faculty of Economics, Hosei University, 4342, Aihara, Machida, Tokyo 194-0298, Japan |
| |
Abstract: | The purpose of this paper is twofold. First, we present the existence theorem of an optimal trajectory in a nonconvex variational problem with recursive integral functionals by employing the norm-topology of a weighted Sobolev space. We show the continuity of the integral functional and the compactness of the set of admissible trajectories. Second, we show that a recursive integrand is represented by a normal integrand under the conditions guaranteeing the existence of optimal trajectories. We also demonstrate that if the recursive integrand satisfies the convexity conditions, then the normal integrand is a convex function. These results are achieved by the application of the representation theorem in Lp-spaces. |
| |
Keywords: | Nonconvexity Recursive integral functional Weighted Sobolev space Carathé odory integrand Nemytskii operator |
本文献已被 ScienceDirect 等数据库收录! |
|