半空间超线性扰动临界诺依曼问题解的存在性

Pub Date : 2024-09-06 DOI:10.1002/mana.202300496
Yinbin Deng, Longge Shi, Xinyue Zhang
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引用次数: 0

摘要

在本文中,我们考虑临界诺依曼问题解的存在性和多重性,其中 , , , , , , 是边界的向外单位法向量,是索波列夫嵌入的通常临界指数,是索波列夫痕量嵌入的临界指数。通过建立改进的 Pohozaev 特性,我们证明如果 .应用无条件山口定理和对山口水平的微妙估计,我们得到了对所有 和 的不同参数值都存在正解。特别是,对于 , , ,我们证明问题()有一个正解,当且仅当 。此外,我们还通过二元变分原理求得了所有且合适的 ()的多解存在。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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Existence of solutions for critical Neumann problem with superlinear perturbation in the half-space

In this paper, we consider the existence and multiplicity of solutions for the critical Neumann problem

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