MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

doi:10.1016/S0252-9602(18)30763-X

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 497-518.doi: 10.1016/S0252-9602(18)30763-X

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

廖家锋^1,2, 蒲洋^1,2, 唐春雷¹

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. School of Mathematics and Information, China West Normal University, Nanchong 637002, China

收稿日期:2016-08-03 修回日期:2017-10-17 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Chunlei TANG E-mail:tangcl@swu.edu.cn
作者简介:Jiafeng LIAO,E-mail:liaojiafeng@163.com;Yang PU,E-mail:172431794@qq.com
基金资助:
Supported by National Natural Science Foundation of China(11471267), the Doctoral Scientific Research Funds of China West Normal University (15D006 and 16E014), Meritocracy Research Funds of China West Normal University (17YC383), and Natural Science Foundation of Education of Guizhou Province (KY[2016]046).

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

Jiafeng LIAO^1,2, Yang PU^1,2, Chunlei TANG¹

1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
2. School of Mathematics and Information, China West Normal University, Nanchong 637002, China

Received:2016-08-03 Revised:2017-10-17 Online:2018-04-25 Published:2018-04-25
Contact: Chunlei TANG E-mail:tangcl@swu.edu.cn
Supported by:
Supported by National Natural Science Foundation of China(11471267), the Doctoral Scientific Research Funds of China West Normal University (15D006 and 16E014), Meritocracy Research Funds of China West Normal University (17YC383), and Natural Science Foundation of Education of Guizhou Province (KY[2016]046).

摘要/Abstract

摘要：

In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,
???20180209???
where Ω ⊂ R^N(N ≥ 3) is an open bounded domain with smooth boundary, 1< q < 2, λ > 0.2^*=2N/N-2 is the critical Sobolev exponent, f ∈L ^{2^*/(2^*-^q)} (Ω) is nonzero and nonnegative, and g ∈ C(Ω) is a positive function with k local maximum points. By the Nehari method and variational method, k +1 positive solutions are obtained. Our results complement and optimize the previous work by Lin[MR2870946, Nonlinear Anal. 75(2012) 2660-2671].

关键词: Semilinear elliptic equations, critical growth, positive solutions, Nehari method, variational method

Abstract:

Key words: Semilinear elliptic equations, critical growth, positive solutions, Nehari method, variational method

廖家锋, 蒲洋, 唐春雷. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH[J]. 数学物理学报(英文版), 2018, 38(2): 497-518.

Jiafeng LIAO, Yang PU, Chunlei TANG. MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH[J]. Acta mathematica scientia,Series B, 2018, 38(2): 497-518.

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MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF CONCAVE-CONVEX ELLIPTIC EQUATIONS WITH CRITICAL GROWTH

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