Geodesic
On solvability of nonlocal boundary value problem for a differential equation of composite type
Matematičeskie zametki SVFU, Tome 28 (2021) no. 4, pp. 90-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the solvability in anisotropic Sobolev spaces of nonlocal in time problems for the differential equations of composite (Sobolev) type $$u_{tt}+\left(\alpha\frac{\partial}{\partial t}+\beta\right)\Delta u+\gamma u=f(x,t),$$ $x = (x_1,\ldots , x_n) \in\Omega\subset R^n$, $t\in(0, T),$ $0 < T < +\infty$, $\alpha, \beta,$ and $\gamma$ are real numbers, and $f(x, t)$ is a given function. We prove theorems of existence and non-existence, uniqueness and non-uniqueness for regular solutions, those having all generalized Sobolev derivatives in the equation.
Keywords: differential equation of composite type, nonlocal problem, regular solution, uniqueness.
Mots-clés : existence 
@article{SVFU_2021_28_4_a6,
     author = {G. I. Tarasova},
     title = {On solvability of nonlocal boundary value problem for a differential equation of composite type},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {90--100},
     year = {2021},
     volume = {28},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2021_28_4_a6/}
}
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G. I. Tarasova. On solvability of nonlocal boundary value problem for a differential equation of composite type. Matematičeskie zametki SVFU, Tome 28 (2021) no. 4, pp. 90-100. http://geodesic.mathdoc.fr/item/SVFU_2021_28_4_a6/