Geodesic
On the existence of time-periodic solutions of nonlinear parabolic differential equations with nonlocal boundary conditions of the
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 4, pp. 712-725

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We study a nonlinear parabolic differential equation in a bounded multidimensional domain with nonlocal boundary conditions of the Bitsadze–Samarskii type. We prove existence theorems for a periodic in time generalized solution. Sufficient conditions for the existence of generalized solutions contain either an algebraic ellipticity condition or an algebraic strong ellipticity condition for the auxiliary differential-difference operator.
Keywords: parabolic differential equation, nonlocal boundary conditions of the Bitsadze–Samarskii type, operator of shifts in spatial variables, pseudomonotone operator. 
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     author = {O. V. Solonukha},
     title = {On the existence of time-periodic solutions of nonlinear parabolic differential equations with nonlocal boundary conditions of the},
     journal = {Contemporary Mathematics. Fundamental Directions},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_4_a10/}
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O. V. Solonukha. On the existence of time-periodic solutions of nonlinear parabolic differential equations with nonlocal boundary conditions of the. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 4, pp. 712-725. http://geodesic.mathdoc.fr/item/CMFD_2023_69_4_a10/