"Uva\u017Eujeme obecn\u00FD neline\u00E1rn\u00ED oper\u00E1tor druh\u00E9ho \u0159\u00E1du v divergentn\u00EDm tvaru. Nejd\u0159\u00EDve se tento oper\u00E1tor definuje na Sobolevov\u011B prostoru funkc\u00ED jedn\u00E9 prom\u011Bnn\u00E9 a jsou prezentov\u00E1ny nutn\u00E9 a posta\u010Duj\u00EDc\u00ED podm\u00EDnky zaru\u010Duj\u00EDc\u00ED jeho monotonii a to jak v obecn\u00E9m, tak v konkr\u00E9tn\u00EDm p\u0159\u00EDpad\u011B. D\u00E1le jsou tyto v\u00FDsledky roz\u0161\u00ED\u0159eny do v\u00EDce prostorov\u00FDch dimenz\u00ED. D\u016Fsledkem je d\u016Fkaz nemonotonie stacion\u00E1rn\u00EDho neline\u00E1rn\u00EDho oper\u00E1toru veden\u00ED tepla v libovoln\u00E9 dimenzi."@cs . "Vejchodsk\u00FD, Tom\u00E1\u0161" . "9"^^ . . "On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form"@en . "577905" . . "A general nonlinear elliptic operator of second order in divergence form is considered. First, the operator is defined on a Sobolev space of functions of one variable, and necessary as well as sufficient conditions ensuring the monotony of the operator are given for both general and particular settings. Next, these results are extended into more spatial dimensions. As a consequence, the nonmonotony of a stationary nonlinear heat conduction operator is proven in an arbitrary spatial dimension."@en . "On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form"@en . "On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form" . . . "nonlinear elliptic operator; divergence form; monotony"@en . "O nemonotonii neline\u00E1rn\u00EDho eleiptick\u00E9ho oper\u00E1toru v divergentn\u00EDm tvaru"@cs . . "A general nonlinear elliptic operator of second order in divergence form is considered. First, the operator is defined on a Sobolev space of functions of one variable, and necessary as well as sufficient conditions ensuring the monotony of the operator are given for both general and particular settings. Next, these results are extended into more spatial dimensions. As a consequence, the nonmonotony of a stationary nonlinear heat conduction operator is proven in an arbitrary spatial dimension." . "1" . "25;33" . "14" . . . . "1343-4373" . "RIV/67985840:_____/04:00022967" . . "Advances in Mathematical Sciences and Applications" . . . "P(IAA1019201), Z(AV0Z1019905)" . . "1"^^ . "O nemonotonii neline\u00E1rn\u00EDho eleiptick\u00E9ho oper\u00E1toru v divergentn\u00EDm tvaru"@cs . . "JP - Japonsko" . "[0C25BAE063D5]" . . "RIV/67985840:_____/04:00022967!RIV06-AV0-67985840" . . "1"^^ . "On the Nonmonotony of Nonlinear Elliptic Operators in Divergence Form" . . .