Positive solutions for the Kirchhoff-type problem involving general critical growth - Part II: 3D numerical solutions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:460

Article

Gu, Cong¹  Yang, Chun-Ming²  Lin, Tai-Chia²  Yeh, Jean¹  Zhang, Huixing³ 

[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

[2] Natl Taiwan Univ, Dept Math, Taipei, Taiwan

[3] China Univ Min & Technol, Sch Math, Xuzhou, Jiangsu, Peoples R China

关键词: Kirchhoff-type problem;    Positive solutions;    Critical nonlinearity;    Numerical solutions;   

DOI  :  10.1016/j.jmaa.2017.09.012

来源: Elsevier

【 摘 要 】

In this paper, we continue the study of the following Kirchhoff-type problem { (a + lambda integral(R3) vertical bar del u vertical bar(2) dx + lambda b integral(R3) vertical bar u vertical bar(2) dx) (-Delta u + bu) = f(u), in R-3, u is an element of H-1 (R-3), u > 0, in R-3, where lambda >= 0 is a parameter, a, b are positive constants and f reaches the critical growth. We use a scaling iterative algorithm to find numerical solutions to the problem on a large enough bounded domain with several particular nonlinearities f, including those with critical growth. We also study the behavior of the solutions as lambda decreases to 0 in consonance with the theoretical study in Part I. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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