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Pairs of positive solutions of quasilinear elliptic equations in exterior domains
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