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We study the existence of solutions u:R3→R2 for the semilinear elliptic systems where W:R2→R is a double well symmetric potential. We use variational methods to show, under generic non-degenerate properties of the set of one dimensional heteroclinic connections between the two minima a± of W, that (0.1) has infinitely many geometrically distinct solutions u∈C2(R3,R2) which satisfy u(x,y,z)→a± as x→±∞ uniformly with respect to (y,z)∈R2 and which exhibit dihedral symmetries with respect to the variables y and z . We also characterize the asymptotic behavior of these solutions as |(y,z)|→+∞. 相似文献
equation(0.1)
−Δu(x,y,z)+∇W(u(x,y,z))=0,
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Let R be the set of real numbers, Y a Banach space and f:R→Y. We prove the Hyers–Ulam stability theorem for the quadratic functional inequality for all (x,y)∈Ω, where Ω⊂R2 is of Lebesgue measure 0. Using the same method we dealt with the stability of two more functional equations in a set of Lebesgue measure 0. 相似文献
‖f(x+y)+f(x−y)−2f(x)−2f(y)‖≤?
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With any -manifold M are associated two dglas and , whose cohomologies and are Gerstenhaber algebras. We establish a formality theorem for -manifolds: there exists an quasi-isomorphism whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the -manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the -manifold M is an isomorphism of Gerstenhaber algebras from to . 相似文献
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