非线性项介于特征值之间的一类抛物方程解的多重性(英文)

Multiplicity Results for a Parabolic Equation with Nonlinearities Crossing Eigenvalues

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.

Muhiplicity 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.