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The existence of solutions to a class of mixed boundary value problems is discussed, when the boundary conditions do not eliminate the possibility of transversal motions of a "non-flexible" plate. Thus one part of the edge may be supported and elastically clamped, another part both elastically supported and clamped, being loaded by transversal loads and moments and the third part is elastically supported without rotations. The edges may have corners and are loaded also by tractions acting in the plane of the plate.
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[2] Hlaváček I., Nečas J.: On inequalities of Korn's type. I. Arch. Ratl. Mech. Anal., 36 (1970), 305-311. DOI 10.1007/BF00249518 | MR 0252844 | Zbl 0193.39001
[3] Lions J. L.: Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris 1969. MR 0259693 | Zbl 0189.40603
[4] Naumann J.: An existence theorem for the von Kármán equations under the conditions of free boundary. Apl. mat., 19 (1974), 17-27. MR 0346294
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