Existence of positive solutions for the nonlinear Kirchhoff type equations in Rn

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Xu, Haoyuan^1,2 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China

关键词: Kirchhoff type equation;    Subcritical exponent;    Positive solution;    Variational method;   

DOI  :  10.1016/j.jmaa.2019.123593

来源: Elsevier

【 摘 要 】

In this paper, we consider the following nonlinear problem of Kirchhoff type: {-(a + lambda integral R-n vertical bar del u vertical bar(2)dx) Delta u + V(x)u = vertical bar u vertical bar(p-1)u, x is an element of R-n, u is an element of H-1(R-n), u > 0, where n >= 3, a, A are positive constants, 1 < p < max(3, n+2/n-2) and V(x) is a positive continuous potential satisfying V-0 < V(x) <= lim inf vertical bar x vertical bar ->infinity V(x) = V-infinity. Using variational methods and a cutoff technique, we prove the existence of positive solution to the above equation for all lambda > 0 small. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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