AN EXISTENCE THEOREM FOR QUASILINEAR SYSTEMS

Proceedings of the Edinburgh Mathematical Society

Haiyan Wang¹ 

关键词: Primary 35J55;    35P65;    p-Laplacian;    elliptic system;    existence;    fixed-point theorem;    cone;   

DOI  :  10.1017/S0013091504001506

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

This paper deals with the existence of positive radial solutions for the quasilinear system $ext{div}(|abla u_i|^{p-2}abla u_i)+lambda f^i(u_1,dots,u_n)=0$, $|x|lt1$, $u_i(x)=0$, on $|x|=1$, $i=1,dots,n$, $pgt1$, $lambda>0$, $xinmathbb{R}^N$. The $f^i$, $i=1,dots,n$, are continuous and non-negative functions. Let $m{u}=(u_1,dots,u_n)$, $|m{u}|=sum_{i=1}^n|u_i|$,$$ f_0^i=lim_{|m{u}|o0}frac{f^i(m{u})}{|m{u}|^{p-1}}, $$$i=1,dots,n$, $m{f}=(f^1,dots,f^n)$, $m{f}_0=sum_{i=1}^nf_0^i$. We prove that the problem has a positive solution for sufficiently small $lambda>0$ if $m{f}_0=infty$. Our methods employ a fixed-point theorem in a cone.

【 授权许可】

Unknown