| 非线性项变号的奇异p-Laplacian动力方程正解的存在性 |
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| 引用本文： | 张红雷,汤建,许方.非线性项变号的奇异p-Laplacian动力方程正解的存在性[J].山西大学学报(自然科学版),2010,33(1). |
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| 作者姓名： | 张红雷 汤建 许方 |
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| 作者单位： | 徐州工程学院数理学院,江苏徐州,221008 |
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| 基金项目： | 江苏省高校自然科学基础研究面上项目，徐州工程学院大学生实践创新训练计划项目 |
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| 摘 要： | 考虑了非线性项是变号的m-点奇异p-Laplacian动力方程(ψ_p(u~'(t)))~'+q(t)f(t,u(t))=0,t∈(0,1),u(0)=0,ψ_p(u'(1))=∑m-2i=1ψi(u~'(ξ_I)),其中ψ~p(s)=|s|~(p-2)s,,p>1,ψ~i:R→R是连续的、不增的,0<ξ_1<ξ_2<…<ξ_(m-2)<1.利用schauder不动点定理和上下解方法,证明了上述边值问题正解的一些存在性法则.作为应用,给出了一个例子验证了主要结果.
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| 关 键 词： | 边值问题 正解 上下解 |
Existence of Positive Solutions to a Singular p-Laplacian Dynamic Equation with Sign Changing Nonlinearity |
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| ZHANG Hong-lei,TANG Jian,XU Fang.Existence of Positive Solutions to a Singular p-Laplacian Dynamic Equation with Sign Changing Nonlinearity[J].Journal of Shanxi University (Natural Science Edition),2010,33(1). |
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| Authors: | ZHANG Hong-lei TANG Jian XU Fang |
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| Institution: | ZHANG Hong-lei,TANG Jian,XU Fang(School of Mathematics , Physical Sciences,Xuzhou Institute of Technology,Xuzhou 221008,China) |
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| Abstract: | Concerned with the following m-point singular p-Laplacian dynamic equation (ψ_p (u~' (t)))~' +q(t)f(t,u(t)) =0,r∈(0,1) ,u(0)=0,ψ_p(u~'(1))=∑m-2i=1ψ_i(u~'(ξ_i)) ,where ψ_p (s) =|s|~(P-2)s,p>1 ,ψ_i :R→R is continuous and nondecreasing,0<ξ_1<ξ_2 <'"<ξ_(m-2) <1. The nonlinearity term is allowed to change sign.By using the Schauder fixed point theorem together with the upper and lower solutions method, some existence criteria are established for positive solutions of the boundary value problem. As an application, an example is given to illustrate these results. |
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| Keywords: | p-Laplacian boundary value problem positive solution p-Laplacian upper and lower solutions |
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