【摘 要】
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Let Xj, j = 1,…, k, be first order smooth quasi-homogeneous vector fields on Rn with the property that the dimension of the Lie algebra generated by these vect
【机 构】
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Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China
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Let Xj, j = 1,…, k, be first order smooth quasi-homogeneous vector fields on Rn with the property that the dimension of the Lie algebra generated by these vector fields is n at x = 0 and X*j = -Xj, j = 1,………, k. Let L = ∑ik=l Xi2. In this paper, we study the nonnegative solutions of semilinear equation Lu +f(x, u) = 0 (or ≤ 0 ) in Rn and generalized cone domain, respectively, and prove that the solutions must be vanish under some suitable conditions.
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