Geodesic
Non-local problems with an integral condition for~third-order differential equations
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 4, pp. 607-620

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The paper is devoted to the study of the solvability of nonlocal problems with an integral variable $t$ condition for the equations $$u_{tt}+\left(\alpha\frac{\partial}{\partial t}+\beta\right)\Delta u=f(x,t)$$ ($\alpha$, $\beta$ are valid constants, $\Delta$ is Laplace operator by spatial variables). Theorems are proved for the studied problems existence and non-existence, uniqueness and non-uniqueness solutions (having all derivatives generalized by S. L. Sobolev included in the equation).
Keywords: third-order differential equations, non-local problems, integral conditions, regular solutions, uniqueness
Mots-clés : existence. 
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     author = {A. I. Kozhanov and A. V. Dyuzheva},
     title = {Non-local problems with an integral condition for~third-order differential equations},
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A. I. Kozhanov; A. V. Dyuzheva. Non-local problems with an integral condition for~third-order differential equations. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 4, pp. 607-620. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_4_a0/