本文主要研究内容
作者（2019）在《A monotonicity theorem and its applications to weighted elliptic equations》一文中研究指出：We study the equation wtt + ?SN-1w-μwt-δw + h（t, ω）wp= 0,（t, ω） ∈ R × SN-1, and under some conditions we prove a monotonicity theorem for its positive solutions. Applying this monotonicity theorem,we obtain a Liouville-type theorem for some nonlinear elliptic weighted singular equations. Moreover, we obtain the necessary and sufficient condition for-div（|x|θ▽u） = |x|lup, x ∈ RN{0} having positive solutions which are bounded near 0, which is also a positive answer to Souplet’s conjecture（see Phan and Souplet（2012）） on the weighted Lane-Emden equation-?u = |x|aup, x ∈ RN.
Abstract
We study the equation wtt + ?SN-1w-μwt-δw + h（t, ω）wp= 0,（t, ω） ∈ R × SN-1, and under some conditions we prove a monotonicity theorem for its positive solutions. Applying this monotonicity theorem,we obtain a Liouville-type theorem for some nonlinear elliptic weighted singular equations. Moreover, we obtain the necessary and sufficient condition for-div（|x|θ▽u） = |x|lup, x ∈ RN{0} having positive solutions which are bounded near 0, which is also a positive answer to Souplet’s conjecture（see Phan and Souplet（2012）） on the weighted Lane-Emden equation-?u = |x|aup, x ∈ RN.
论文参考文献
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：A monotonicity theorem and its applications to weighted elliptic equations论文
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