| 具有N-各向异性拉普拉斯算子的超线性问题的先验界 |
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| 引用本文： | 裴瑞昌.具有N-各向异性拉普拉斯算子的超线性问题的先验界[J].数学学报,2017,60(5):823-832. |
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| 作者姓名： | 裴瑞昌 |
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| 作者单位： | 天水师范学院数学与统计学院 天水 741000 |
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| 基金项目： | 国家自然科学基金（11661070，11561059）；甘肃省自然科学基金（1506RJZE114，1606RJYE237） |
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| 摘 要： | 通过改进Brezis和Merle的方法,结合Moser-Trudinger不等式,移动平面方法及比较原理,得到了方程-Q_Nu=f(u),u∈W_0~(1,N)(Ω)的正解的先验界,其中Ω是R~N中的一个有界光滑区域,非线性项f至多具有指数型增长.
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| 关 键 词： | QN-拉普拉斯算子 移动平面 先验界 Moser-Trudinger不等式 |
A Priori Bounds for Superlinear Problems Involving the N-anisotropic Laplacian Operator |
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| Rui Chang PEI.A Priori Bounds for Superlinear Problems Involving the N-anisotropic Laplacian Operator[J].Acta Mathematica Sinica,2017,60(5):823-832. |
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| Authors: | Rui Chang PEI |
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| Institution: | School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741000, P. R. China |
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| Abstract: | We establish a priori bounds for positive solutions of the equation -QNu=f(u),u∈W01,N(Ω), where Ω is a bounded smooth domain in RN, and the nonlinearity f has at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis and Merle to the QN-Laplacian, in combination with the Moser-Trudinger inequality, the Moving Planes method and a Comparison Principle for the QN-Laplacian. |
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| Keywords: | QN-Laplacian moving planes priori bounds Moser-Trudinger inequality |
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