Pairs of positive solutions of quasilinear elliptic equations in exterior domains

Takaŝi Kusano, Charles Swanson, Hiroyuki Usami
1985 Pacific Journal of Mathematics  
Our main objective is to prove the existence of infinitely many pairs (Wj, u 2 ) of positive solutions of quasilinear elliptic differential equations throughout exterior domains Q a c R^, N > 2, of the type Q a = {JCGR^: |JC|> a), a> 0, where x = (JC 1 ,...,X ;V ), Vw -(du/dx l9 ... ,du/dx N ), and Δ = v * V Each pair has the property that u ι (x)/u 2 (x) has uniform limit zero in Ω α as jjcj -» oo. In particular, if q(t) s 0 and N > 3, u x (x) has limit 0 as |x| ~> oo, and u 2 (x) is bounded above and below by positive constants in
doi:10.2140/pjm.1985.120.385 fatcat:hzs6lkvjdrelvja4wvjlz4yxoy