测度链上p-Laplacian算子的Sturm—Liouville边值问题的正解

张克玉, 王建国, 徐家发

数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 993-1000.

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数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 993-1000. DOI: 10.12386/A2014sxxb0092
论文

测度链上p-Laplacian算子的Sturm—Liouville边值问题的正解

    张克玉1, 王建国1, 徐家发2
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Positive Solutions for p-Laplacian Sturm-Liouville Boundary Value Problems on Time Scales

    Ke Yu ZHANG1, Jian Guo WANG1, Jia Fa XU2
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摘要

利用锥上的不动点定理，研究了测度链上四阶 p-LaplacianSturm-Liouville 边值问题

正解的存在性，得到了至少存在两个正解的充分条件. 这里 p >1 且f：[p（a）b]×R+→R+（R+：=[0，∞））连续.

Abstract

We investigate the existence of two positive solutions for the following fourth order p-Laplacian Sturm-Liouville boundary value problems on time scales
 
Here p > 1 and f: [ρ(a), b] × R+ → R+(R+:= [0,∞)) is continuous. Under sufficient growth conditions on the nonlinearity f and by virtue of fixed point theorems on cones, we obtain at least two positive solutions for the above problem.

关键词

测度链 / p-Laplacian 方程 / 正解 / 不动点定理

Key words

time scales / p-Laplacian equation / positive solution / fixed point theorem

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张克玉, 王建国, 徐家发. 测度链上p-Laplacian算子的Sturm—Liouville边值问题的正解. 数学学报, 2014, 57(5): 993-1000 https://doi.org/10.12386/A2014sxxb0092
Ke Yu ZHANG, Jian Guo WANG, Jia Fa XU. Positive Solutions for p-Laplacian Sturm-Liouville Boundary Value Problems on Time Scales. Acta Mathematica Sinica, Chinese Series, 2014, 57(5): 993-1000 https://doi.org/10.12386/A2014sxxb0092

参考文献

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基金

国家自然科学基金资助项目（10971046）；山东省自然科学基金资助项目（ZR2012AQ007）及山东省高等学校科技计划项目（J09LA55）

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