References
R. Finn, “On a problem of type with applications to elliptic partial differential equations,” J. Rat. Mech. Anal., No. 3, 789–799 (1954).
J. B. Keller, “On solution of Δu=f(u),” Commun. Pure Appl. Math.,10, No. 4, 503–510 (1957).
R. Osserman, “On the inequality Δu≥f(u),” Pac. J. Math.,7, No. 4, 1641–1647 (1957).
S. I. Pokhozhaev, “On the boundary-value problem of the equation Δu=u2,” Dokl. Akad. Nauk SSSR,140, No. 3, 518–521 (1961).
L. Veron, “Comportement asymptotique des solutions d'equations elliptiques seimilineaires dans PN,” Ann. Math. Pura Appl.,127, 25–50 (1981).
L. Veron, “Singular solution of some nonlinear elliptic equation,” Nonlinear Anal.,5, No. 3, 225–249 (1981).
H. Brezis and L. Veron, “Removable singularities for some nonlinear elliptic equations,” Arch. Rat. Mech. Anal.,75, No. 1, 1–6 (1980).
V. A. Kondrat'ev and E. M. Landis, “On qualitative properties of solutions of nonlinear equations of second order,” Mat. Sb.,135(177), No. 3, 346–360 (1977).
V. A. Kondrat'ev and E. M. Landis, “Semilinear equations of second order with nonnegative characteristic forms,” Mat. Zametki,44, No. 3, 475–468 (1988).
R. Finn, Equilibrium Capillary Surfaces, Springer-Verlag, New York (1986).
V. M. Gol'dstein and Yu. G. Peshetnyak, Introduction to the Theory of Functions with Generalized Derivatives and Quasiconformal Mappings [in Russian], Nauka, Moscow (1983).
S. Y. Cheng and S. T. Yau, “Differential equations on Riemannian manifolds and their geometric applications,” Commun. Pure Appl. Math.,28, No. 3, 333–354 (1975).
V. G. Tkachev, “Extrinsic construction of minimal surfaces of parabolic type,” Candidate's Dissertation, Math.-Physical Science, Novosibirsk (1990).
J. Serrin, “Local behaviour of solutions of quasilinear equations,” Acta Math.,111, 247–302 (1964).
J. Hwang, “Comparison principle and Liouville theorems for prescribed mean curvature equations in unbounded domains,” Annali Scuola Norm. Sup. Pisa, Ser. 4,15, No. 3, 341–355 (1988).
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Translated from Matematicheskie Zametki, Vol. 53, No. 4, pp. 53–61, April, 1993.
In conclusion with sincere gratitude I express my appreciation to E. M. Landis and V. M. Miklyukov for their useful discussions on the work.
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Kurta, V.V. On the uniqueness of the Dirichlet problem of the mean curvature equation. Math Notes 53, 394–399 (1993). https://doi.org/10.1007/BF01210222
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DOI: https://doi.org/10.1007/BF01210222