赋范空间中一个二次方程解的个数（英文）

On the number of solutions of a quadratic equation in a normed space

研究方程Q(u)=g,其中Q是映射一个赋范空间到另一个的连续二次算子。显然,若u是该方程的一个解,则-u也是一个解。给出没有其它解的条件,并应用其研究偏微方程uΔu=g的Dirichlet边值问题。

Consider the equation Q（u） = g,where Q is a continuous quadratic operator acting from one normed space to another one.Obviously,if u is a solution of such equation,then-u is also a solution.Conditions implying that there are no other solutions are given and applied to the study of the Dirichlet boundary value problem for the partial differential equation uΔu = g.