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A note on the Neumann problem for a quasilinear elliptic problem of a nonmonotone type. (English) Zbl 0876.35041
Summary: The existence and uniqueness of a weak solution of a Neumann problem is discussed for a second-order quasilinear elliptic equation in divergence from. The note is a continuation of a recent paper, where mixed boundary value problems were considered, which guaranteed the coerciveness of the problem.

35J65Nonlinear boundary value problems for linear elliptic equations
Full Text: DOI
[1] Hlaváček, I.; Křı\acute{}žek, M.; Malý, J.: On Galerkin approximations of a quasilinear nonpotential elliptic problem of a nonmonotone type. J. math. Anal. appl. 184, 168-189 (1994) · Zbl 0802.65113
[2] Hlaváček, I.; Nečas, J.: On inequalities of korn’s type, I. Arch. rational mech. Anal. 36, 305-311 (1970) · Zbl 0193.39001
[3] Nečas, J.: LES méthodes directes en théorie des équations elliptiques. (1967)