Liouville Type Theorems of Semilinear Equations with Square Sum of Vector Fields

Liouville Type Theorems of Semilinear Equations with Square Sum of Vector Fields

Year:    2005

Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 2 : pp. 149–153

Abstract

Let X_j ; 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 = -X_j, j = 1, …, k. Let L = \sum^k_{i=1} X²_i . 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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2005-JPDE-5351

Journal of Partial Differential Equations, Vol. 18 (2005), Iss. 2 : pp. 149–153

Published online:    2005-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    5

Keywords:    Liouville type theorem