| 一类拟线性抛物方程的周期解(英文) |
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| 引用本文： | 王佩臣,郭秀颖,郭巧栋,范广慧.一类拟线性抛物方程的周期解(英文)[J].黑龙江大学自然科学学报,2012,29(2):216-218. |
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| 作者姓名： | 王佩臣 郭秀颖 郭巧栋 范广慧 |
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| 作者单位： | 黑龙江工程学院教学系,哈尔滨,150001 |
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| 基金项目： | Supported by the Natural Sciences Foundation of Heilongjiang Province(QC2011C020);the Fund of Heilongjiang Province Education Committee(11551134) |
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| 摘 要： | 研究一类拟线性抛物方程的Dirichlet边值问题。由于方程的非线性及退化性,只考虑问题弱解的存在性。如何构造出一对有序的上下解也是得到非平凡非负周期解的关键所在。利用p-Laplacian算子的第一特征值和相应的特征函数,构造出满足定义的一对有序的周期上下解,从而利用单调迭代方法给出上述周期边值问题非平凡非负周期解的存在性。
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| 关 键 词： | 拟线性 周期解 存在性 |
Periodic solutions of a class of quasilinear parabolic equations |
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| WANG Pei-chen
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GUO Xiu-ying
,
GUO Qiao-dong
,
FAN Guang-hui.Periodic solutions of a class of quasilinear parabolic equations[J].Journal of Natural Science of Heilongjiang University,2012,29(2):216-218. |
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| Authors: | WANG Pei-chen GUO Xiu-ying GUO Qiao-dong FAN Guang-hui |
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| Institution: | (Department of Mathematics,Heilongjiang Institute of Technology,Harbin 150001,China) |
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| Abstract: | The Dirichlet boundary value problem of a class of quasilinear parabolic equations with periodic reaction term is considered.Since the equation is nonlinear and degenerate,the existence of the weak solutions of the problem is only involved.The key is how to construct a pair of ordered supersolution and subsolution.By using the first eigenvalue and the corresponding eigenfunction of the p-Laplacian,a pair of ordered T-periodic supersolution and subsolution is constructed.Then by using the monotonicity method,the existence of nontrivial nonnegative periodic solutions is obtained. |
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| Keywords: | quasilinear periodic solutions existence |
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