非线性项介于特征值之间的一类抛物方程解的多重性
비선성항개우특정치지간적일류포물방정해적다중성
Multiplicity Results for a Parabolic Equation with Nonlinearities Crossing Eigenvalues
  • 万方数据
    郑州大学学报（理学版） 정주대학학보（이학판）
    JOURNAL OF ZHENGZHOU UNIVERSITY(NATURAL SCIENCE EDITION)
    2008年 3期 6-10 ,共5页

    燕艳菊%杨金花%金正国

    연염국%양금화%금정국

    特征值%压缩映象原理%变分方法 特徵值%壓縮映象原理%變分方法
    특정치%압축영상원리%변분방법
    eigenvalue contraction mapping theorem%variational reduction method
    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.
    고찰료재유계구역상,만족적리극래변계조건적일류비선성포물방정.이용변분방법이론,파무한유적문제전화위유한유적문제,토론료당방정적비선성항개우특정치지간시,방정적외부항여방정해적다중성지간적련계.
    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.
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