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.


35J65 Nonlinear boundary value problems for linear elliptic equations
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[1] Hlaváček, I.; Křı́žek, 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), Academia - Masson Prague - Paris · Zbl 1225.35003
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