| 具非线性边值条件的发展型p-Laplace方程解在有限时刻的爆破性和有界性 |
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| 引用本文： | 王建,高文杰.具非线性边值条件的发展型p-Laplace方程解在有限时刻的爆破性和有界性[J].吉林大学学报(理学版),2005,43(4):395-401. |
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| 作者姓名： | 王建 高文杰 |
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| 作者单位： | 吉林大学,数学研究所,长春,130012;吉林大学,数学研究所,长春,130012 |
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| 基金项目： | 国家自然科学基金(批准号:10371050). |
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| 摘 要： | 讨论具非线性边值条件的发展型p-Laplace方程解
的爆破性和有界性. 给出了一维情形下的比较原理; 通过构造特殊形式的上下解找到一维情
形下解在有限时刻爆破和有界的条件, 并研究了高维情形的径向解在有限时刻爆破或有界的
结果; 文中例子表明所得结果是非平凡的.
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| 关 键 词： | 非线性 边值问题 p-Laplace 爆破 |
| 文章编号： | 1671-5489(2005)04-0395-07 |
| 收稿时间： | 2005-01-11 |
| 修稿时间： | 2005年1月11日 |
Blow-up and Boundedness of Solutions at Finite Time for Evolution p-Laplace Equations with Nonlinear Boundary Conditions |
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| WANG Jian,GAO Wen-jie.Blow-up and Boundedness of Solutions at Finite Time for Evolution p-Laplace Equations with Nonlinear Boundary Conditions[J].Journal of Jilin University: Sci Ed,2005,43(4):395-401. |
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| Authors: | WANG Jian GAO Wen-jie |
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| Institution: | Institute of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | The present paper studied the blow-up and boundedness of solutions at finite time for evolution (p-Laplace) equations with nonlinear boundary conditions. The authors firstly proved a comparison principle in one dimension case and then found some conditions under which the solutions may blow-up at finite time. The authors also gave some conditions under which the solutions will be bounded at any finite time. Similar results to the radial solutions of the equation in higher dimension case are also mentioned. In the last section, a (special) example is presented to show that the theorems are applicable. |
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| Keywords: | nonlinear boundary value problem p-Laplace blow-up |
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