关于方程-Δu+f(x,u)=h的一个新结果

A New Result about Equation-Δu+f(x,u)=h

该文研究二阶半线性椭圆型方程 -Δu+ f(x ,u) =h的Dirichlet问题弱解的存在性和唯一性。采用同胚的观点把问题转化为非线性算子 -Δ+ f(x ,·)的延拓性。用延拓方法得到了关于解存在的一个充分必要条件和解唯一的一个充分条件。这些条件是整体积分形式的。该研究不但是用了新的方法 。

Existence and uniqueness of a second order semilinear equation - Δ u+f(x,u)=h is considered. The view of homeomorphism being taken, the problem is converted into the continuation property of the nonlinear operator - Δ +f(x,·). A necessary and sufficient condition for the existence and a sufficient condition for the uniqueness, which are in a global form of integral, are obtained by the continuation method. The research is not only made in a new way, but also generalizes some results of other authors to some extent.