# Partial symmetry and asymptotic behavior for some elliptic variational problems

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In this paper, we establish Lyapunov-type inequalities for two classes of difference systems which improve all existing ones in the literature. Applying our inequalities, we obtain a lower bound for the eigenvalues of corresponding systems.

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In this paper, we establish an equivalent statement to minimax inequality for a special class of functionals. As an application, we prove the existence of three solutions to the Dirichlet problem -u" (x) + m(x)u(x) = Î»f(x, u(x)), x âˆˆ (a, b), u(a) = u(b) = 0, where Î» > 0, f : [a, b] X...

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We consider the Dirichlet problem for biharmonic maps u from a bounded, smooth domain $${\Omega\subset\mathbb R^n (n\ge 5)}$$ to a compact, smooth Riemannian manifold $${N\subset{\mathbb {R}}^l}$$ without boundary. For any smooth boundary data, we show that if u is a stationary biharmonic map...