Existence and asymptotic behavior of ground state solutions of semilinear elliptic system

Advances in Nonlinear Analysis

article

Habib Mâagli¹  Sonia Ben Othman²  Safa Dridi² 

[1] King Abdulaziz University, College of Sciences and Arts, Rabigh Campus, Department of Mathematics;Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire

关键词: Semilinear elliptic system;    asymptotic behavior;    Karamata class;    ground state solution;    subsolution;    supersolution;   

DOI  :  10.1515/anona-2015-0157

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In this article, we take up the existence and the asymptotic behavior of entire bounded positive solutions to the following semilinear elliptic system: -Δ u = a1a_{1}( x )uαu^{\alpha}vrv^{r}, x ∈\inℝn\mathbb{R}^{n} ( n ≥\geq 3), -Δ v = a2a_{2}( x )vβv^{\beta}usu^{s}, x ∈\inℝn\mathbb{R}^{n}, u , v ¿ 0 in ℝn\mathbb{R}^{n}, lim|x|→+∞\lim_{|x|\rightarrow+\infty} u ( x ) = lim|x|→+∞\lim_{|x|\rightarrow+\infty} v ( x )=0, where α,β0{\nu:=(1-\alpha)(1-\beta)-rs>0}, and the functions a1a_{1}, a2a_{2} are nonnegative in ?locγ⁢(ℝn){\mathcal{C}^{\gamma}_{\mathrm{loc}}(\mathbb{R}^{n})} (0¡γ¡1) and satisfy some appropriate assumptions related to Karamata regular variation theory.

【 授权许可】

CC BY