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| 非线性项介于特征值之间的一类抛物方程解的多重性 | |
| 引用本文： | 燕艳菊,杨金花,金正国.非线性项介于特征值之间的一类抛物方程解的多重性[J].郑州大学学报(理学版),2008,40(3). |
| 作者姓名： | 燕艳菊 杨金花 金正国 |
| 作者单位： | 1. 安阳工学院理学部,河南,安阳,455000 2. 周口师范学院数学系,河南,周口,466001 3. 大连理工大学应用数学系,辽宁,大连,116024 |
| 摘 要： | 考察了在有界区域上,满足狄利克莱边界条件的一类非线性抛物方程.利用变分方法理论,把无限维的问题转化为有限维的问题,讨论了当方程的非线性项介于特征值之间时,方程的外部项与方程解的多重性之间的联系. |
| 关 键 词： | 特征值 压缩映象原理 变分方法 |
Multiplicity Results for a Parabolic Equation with Nonlinearities Crossing Eigenvalues |
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| YAN Yan-ju,YANG Jin-hua,JIN Zheng-guo.Multiplicity Results for a Parabolic Equation with Nonlinearities Crossing Eigenvalues[J].Journal of Zhengzhou University:Natural Science Edition,2008,40(3). | |
| Authors: | YAN Yan-ju YANG Jin-hua JIN Zheng-guo |
| Abstract: | Multiplicity of solutions for a nonlinear perturbation of a parabolic operator under Dirichlet boundary condition in a bounded domain is investigated.The variational reduction method is used to reduce the problem from an infinite dimensional one to a finite one,and then a relationship between multiplicity of solution and source terms in equation is revealed when nonlinearities cross eigenvalues. |
| Keywords: | eigenvalue contraction mapping theorem variational reduction method |
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