A monotonicity theorem and its applications to weighted elliptic equations

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（10）
• 页码范围: 1925-1934
• 页数: 10页
• 语种: 英文

摘要

We study the equation wtt+ △SN-1w-μwt-δw + h(t,w)wp =0,(t,w) ∈ 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.