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- W2885904167 abstract "In the current paper, in the domain $D={(t,x): tin(0,T), xin(0,L)}$ we investigate the boundary value problem for the equation of motion of a homogeneous elastic beam $$ u_{tt}(t,x)+a^{2}u_{xxxx}(t,x)+b u_{xx}(t,x)+c u(t,x)=0, $$ where $a,b,c in mathbb{R}$, $b^2<4a^2c$, with nonlocal two-point conditions $$u(0,x)-u(T, x)=varphi(x), quad u_{t}(0, x)-u_{t}(T, x)=psi(x)$$ and local boundary conditions $$u(t, 0)=u(t, L)=u_{xx}(t, 0)=u_{xx}(t, L)=0.$$ Solvability of this problem is connected with the problem of small denominators, whose estimation from below is based on the application of the metric approach. For almost all (with respect to Lebesgue measure) parameters of the problem, we establish conditions for the solvability of the problem in the Sobolev space. In particular, if $varphiinmathbf{H}_{q+rho+2}$ and $psi inmathbf{H}_{q+rho}$, where $rho>2$, then for almost all (with respect to Lebesgue measure in $mathbb{R}$) numbers $a$ exists a unique solution $uinmathbf{C}^{,2}([0,T];mathbf{H}_{q})$ of the problem considered." @default.
- W2885904167 created "2018-08-22" @default.
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- W2885904167 date "2018-07-03" @default.
- W2885904167 modified "2023-09-26" @default.
- W2885904167 title "On nonlocal boundary value problem for the equation of motion of a homogeneous elastic beam with pinned-pinned ends" @default.
- W2885904167 doi "https://doi.org/10.15330/cmp.10.1.105-113" @default.
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