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1.
M. N. Yakovlev 《Journal of Mathematical Sciences》2007,141(6):1710-1722
It is proved that the boundary-value problem
, has a solution, provided that the following conditions are fulfilled:
, and, for ϕ(u) ≡ 0, the Galerkin method converges in the norm of the space H1(a, b; a). Several theorems of a similar kind are presented. Bibliography: 4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 246–266. 相似文献
2.
Yu. Kh. Eshkabilov 《Siberian Advances in Mathematics》2009,19(4):233-244
Let Ω1, Ω2 ⊂ ℝν be compact sets. In the Hilbert space L
2(Ω1 × Ω2), we study the spectral properties of selfadjoint partially integral operators T
1, T
2, and T
1 + T
2, with
$
\begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered}
$
\begin{gathered} (T_1 f)(x,y) = \int_{\Omega _1 } {k_1 (x,s,y)f(s,y)d\mu (s),} \hfill \\ (T_2 f)(x,y) = \int_{\Omega _2 } {k_2 (x,t,y)f(x,t)d\mu (t),} \hfill \\ \end{gathered}
相似文献
3.
Yoshitaka Uda 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1995,46(3):366-383
We study nonnegative solutions of the initial value problem for a weakly coupled system
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