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On the number of solutions of a quadratic equation in a normed space. (English) Zbl 1349.39040
Summary: This paper considers 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 \(u\Delta u = g\).
39B42 Matrix and operator functional equations
35J60 Nonlinear elliptic equations
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