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" The main result of this section is given by the following theorem. Theorem 4.3. "
Nonsmooth Variational Problems and Their Inequalities: Comparison Principles ... - Page 182
by Siegfried Carl, Vy Khoi Le, Dumitru Motreanu - 2007 - 398 pages
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Enumerative Combinatorics: Volume 2

Richard P. Stanley - Mathematics - 1997 - 600 pages
...(where is a Laurent monomial in x\, . . . . xk) is a kind of "generalized noncommutative diagonal." The main result of this section is given by the following theorem. 6.7.1 Theorem. Let S = S(X, Y) be given by (6.52). Suppose that S(X, X~') is well-defined formally,...
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Partial Differential Equations: Mark Vishik's Seminar, Volume 206

M. S. Agranovich - Mathematics - 2002 - 292 pages
...approximate y by y* € H* n BR. The operator Gi(X. Dmi u) can be studied similarly. The lemma is proved. D The main result of this section is given by the following theorem. THEOREM 7.9. Suppose that the operator F(x.D2m) is uniformly elliptic and that the Shapiro Lopatin.shi conditions...
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Monotone Flows and Rapid Convergence for Nonlinear Partial Differential ...

V. Lakshmikantham, S. Koksal - Mathematics - 2003 - 336 pages
...in the ordered interval [QO,/3O] formed by the lower and upper solutions c*o and /3o, respectively. The main result of this section is given by the following theorem. Theorem 6.5.1 Let hypotheses (Hl)-(H3) be satisfied. Then there exist monotone sequences (аn)^=i, (n)^=i...
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Exactly Solvable Models of Biological Invasion

Sergei V. Petrovskii, Bai-Lian Li - Mathematics - 2005 - 242 pages
...is equivalent to assumption (6.26). That proves the theorem. 6.1.2 Exact solution and its properties The main result of this section is given by the following theorem: Theorem 6.3. Under constraints (6.10-6.11) and k > 2^/m, the system (6.8-6.9) has the following exact solution:...
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Stabilization of the Index for Elliptic Problems

Vitaly Volpert - Differential equations, Elliptic - 2007 - 88 pages
...is formally adjoint to the operator L*. Therefore dim Ker(L) > dim Ker(L*). The corollary is proved. The main result of this section is given by the following theorem. Theorem 4.3. Suppose that the dimension of the kernel of the operator Ln equals fi and the codimension of the...
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