） Abstract： This paper is concerned with the existence of multiple positive solutions for(ω(t)ψp(u'(t)))'+h(t)f(t,u(t),u'(t))=o,t∈(0,+∞);u(0)/1+l(0)=βlim t→0+(ψ -1 p(ω)u')(t),lim t→+∞(ψ -1 p(ω)u')(t)=0; where ω∈C((0,+∞),(0,+∞)), ψp(s)=|s|p-2, p>1,β≥0, both h(t) and f(t,u,v) are nonnegative continuous functions thatmay be singular at t=0, l(t)=∣t0 ψ p -1(1/ω)ds
By usinga fixed point theorem due to Avery and Peterson, some sufficient conditions forthe existence of at least three positive solutions to the above problem areestablished
The interesting points are that the weight function $omega$ isassumed to satisfy ψ p -1(1/ω)∈L1(0,b) for all b∈(0,+∞)$rather than ψ p -1(1/ω)∈L1(0,+∞) and the nonlinear term f is involved with the first-order derivative explicitly
Keywords： Weighted p-Laplacian; Three Positive Solutions; Fixed Point Theorem; Weighted Banach Space 下载PDF阅读器 PDF全文下载： 初稿 （ 138 ） 原始数据 作者简介： Song Huijuan, (1985-), female, Ph
D
student, major research direction:nonlinear diffusion equations
通信联系人： Yang Ying, (1983-), female, instructor, major research direction:nonlinear diffusion equations
【收录情况】 中国科技论文在线： Song Huijuan
Yang Ying 3,* （ 1、 Department of Mathematics, Jilin University, ChangChun 130012
） 摘要： This paper is concerned with the existence of multiple positive solutions for(ω(t)ψp(u'(t)))'+h(t)f(t,u(t),u'(t))=o,t∈(0,+∞);u(0)/1+l(0)=βlim t→0+(ψ -1 p(ω)u')(t),lim t→+∞(ψ -1 p(ω)u')(t)=0; where ω∈C((0,+∞),(0,+∞)), ψp(s)=|s|p-2, p>1,β≥0, both h(t) and f(t,u,v) are nonnegative continuous functions thatmay be singular at t=0, l(t)=∣t0 ψ p -1(1/ω)ds
By usinga fixed point theorem due to Avery and Peterson, some sufficient conditions forthe existence of at least three positive solutions to the above problem areestablished
The interesting points are that the weight function $omega$ isassumed to satisfy ψ p -1(1/ω)∈L1(0,b) for all b∈(0,+∞)$rather than ψ p -1(1/ω)∈L1(0,+∞) and the nonlinear term f is involved with the first-order derivative explicitly
关键词： Weighted p-Laplacian; Three Positive Solutions; Fixe Point Theorem; Weighted Banach Space Song Huijuan 1,
2、 School of Mathematical Sciences, South China Normal University, GuangZhou 510631
2、 School of Mathematical Sciences, South China Normal University, GuangZhou 510631
3、 College of Mathematics and Computational Science, Shenzhen University, GuangDong ShenZhen 518060
3、 College of Mathematics and Computational Science, Shenzhen University, GuangDong ShenZhen 518060
* （ 1、 Department of Mathematics, Jilin University, ChangChun 130012
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