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The solutions of the coupled Einstein-Maxwell equations and Dilaton equations. (English) Zbl 1400.35141
Summary: In this paper, we consider extremely charged static perfect fluid distributions with a dilaton field in the framework of general relativity. By using calculus of variations, we establish the existence theorem for the solutions of this important gravitational system. We show that there is a continuous family of smooth solutions realizing asymptotically flat space metrics.
MSC:
35J91 Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian
83C22 Einstein-Maxwell equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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