含一般非线性项Kirchhoff型约束变分问题Schwarz对称极小解的存在性

Existence of Schwarz symmetric minimizers for a Kirchhoff constrained variational problem with general nonlinear term

利用约束变分理论和对称递减重排技巧考虑一般非线性项情形下一类Kirchhoff型约束变分问题Schwarz对称极小解的存在性和不存在性.针对非线性项的指数和约束∫R^(N)|u|^(2)dx=c^(2)中的c与极小化问题Schwarz对称极小解存在与否的关系,得到了一个细致明确的划分.

In this paper,by using the theory of constrained variational and symmetric decreasing rearrangement technique,the existence and nonexistence of Schwarz symmetric minimizers of a class of Kirchhoff constrained variational problem with a general nonlinear term were considered.Especially,a complete classification of the existence and nonexistence for Schwarz symmetric minimizers with respect to the exponent in nonlinear term and c in manifold ∫R^(N)|u|^(2)dx=c^(2) was obtained.