Geodesic
On a~class of essentially nonlinear elliptic differential--difference equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 233-251

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An essentially nonlinear differential-difference equation containing the product of the $p$-Laplacian and a difference operator is considered. Sufficient conditions are obtained for the corresponding nonlinear differential-difference operator to be coercive and pseudomonotone in the case of nonvariational statement of the differential equation. The existence of a generalized solution to the Dirichlet problem for the nonlinear equation is proved. 
@article{TM_2013_283_a14,
     author = {O. V. Solonukha},
     title = {On a~class of essentially nonlinear elliptic differential--difference equations},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {233--251},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_283_a14/}
}
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O. V. Solonukha. On a~class of essentially nonlinear elliptic differential--difference equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 233-251. http://geodesic.mathdoc.fr/item/TM_2013_283_a14/