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On a boundary value problem in nonlinear theory of thin elastic plates. (English) Zbl 0295.73056


MSC:

74K20 Plates
35Q99 Partial differential equations of mathematical physics and other areas of application
74S30 Other numerical methods in solid mechanics (MSC2010)
74B20 Nonlinear elasticity
49J20 Existence theories for optimal control problems involving partial differential equations
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References:

[1] Knightly G. H.: An existence theorem for the von Kármán equations. Arch. Rat. Mech. Anal., 27 (1967), 233-242. · Zbl 0162.56303 · doi:10.1007/BF00290614
[2] Knightly G. H., Sather D.: On nonuniqueness of solutions of the von Kármán equations. Arch. Rat. Mech. Anal., 36 (1970), 65-78. · Zbl 0188.57603 · doi:10.1007/BF00255747
[3] Langenbach A.: Über Gleichungen mit Potentialoperatoren und Minimalfolgen nichtquadratischer Funktionale. Math. Nachr., 32 (1966), 9 - 24. · Zbl 0154.39903 · doi:10.1002/mana.19660320103
[4] Morozov N. F.: Nonlinear problems in the theory of thin plates. (Russian). Vestnik Leningr. Univ., 19 (1958), 100-124.
[5] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. · Zbl 1225.35003
[6] Nečas J., Poracká Z., and Kodnar R.: Remarks on a nonlinear theory of thin elastic plates. Matem. časopis, 20 (1970), 62-71. · Zbl 0206.53606
[7] Sharij Ju. I., Jurchenko A. S.: Dirichlet’s problem for equations of Karman’s type. Diff. urav., 4 (1968), 1713-1719.
[8] Vorovich I. I.: On the existence of solutions in nonlinear theory of shells. (Russian). Izv. Akad. Nauk, ser. mat., 19, no. 4 (1955), 173-186. · Zbl 0065.17903
[9] Vorovich I. I.: On some direct methods in nonlinear theory of shallow shells. (Russian). Prikl. Mat. Mech., 20 (1956), 449-474. · Zbl 0075.32707
[10] Vorovich I. I.: On the existence of solutions in nonlinear theory of shells. (Russian). Dokl. Akad. Nauk, SSSR, 117 (1957), 203-206. · Zbl 0091.39702
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