Nonlinear differential-difference equations of elliptic and parabolic type and their applications to nonlocal problems

O. V. Solonukha

Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 3, pp. 445-563.

Résumé

In this survey, we study boundary-value problems for nonlinear differential-difference equations of elliptic and parabolic types, as well as related nonlinear equations with nonlocal boundary conditions. The main feature of the equations under consideration is that the difference operator is located in the principal part of the nonlinear operator containing higher-order derivatives.

Détail

Keywords: nonlinear differential-difference equations, nonlocal boundary conditions, shift in spatial variables, initial-boundary value problem, periodic solutions, pseudomonotone operator, operator with semi-bounded variation, ellipticity condition, strong ellipticity condition.
Mots-clés : elliptic equation, parabolic equation

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