共查询到2条相似文献,搜索用时 0 毫秒
1.
Soon-Mo Jung 《数学学报(英文版)》2010,26(11):2085-2092
We prove a global version of the implicit function theorem under a special condition and apply this result to the proof of a modified Hyers-Ulam-Rassias stability of exact differential equations of the form, g(x, y) + h(x, y)y' =0. 相似文献
2.
Sheng-Ming Ma 《数学学报(英文版)》2009,25(11):1865-1874
This paper proves a theorem on the decay rate of the oscillatory integral operator with a degenerate C^∞ phase function, thus improving a classical theorem of HSrmander. The proof invokes two new methods to resolve the singularity of such kind of operators: a delicate method to decompose the operator and balance the L^2 norm estimates; and a method for resolution of singularity of the convolution type. The operator is decomposed into four major pieces instead of infinite dyadic pieces, which reveals that Cotlar's Lemma is not essential for the L^2 estimate of the operator. In the end the conclusion is further improved from the degenerate C^∞ phase function to the degenerate C^4 phase function. 相似文献