Geodesic
On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator
Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 604-620

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An essentially nonlinear equation containing the product of the $p$-Laplacian and a nonsymmetric difference operator is considered. Sufficient conditions guaranteeing the coercivity and pseudomonotonicity of the corresponding nonlinear difference-differential operator are obtained. The existence of a generalized solution of the Dirichlet problem for the nonlinear equation under consideration is proved.
Keywords: essentially nonlinear elliptic functional-differential equation, pseudomonotone operator, accretive operator. 
@article{MZM_2018_104_4_a8,
     author = {O. V. Solonukha},
     title = {On an {Elliptic} {Differential-Difference} {Equation} with {Nonsymmetric} {Shift} {Operator}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {604--620},
     publisher = {mathdoc},
     volume = {104},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a8/}
}
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O. V. Solonukha. On an Elliptic Differential-Difference Equation with Nonsymmetric Shift Operator. Matematičeskie zametki, Tome 104 (2018) no. 4, pp. 604-620. http://geodesic.mathdoc.fr/item/MZM_2018_104_4_a8/