A Class Of Semi-linear Elliptic Systems Of Non-existence Of Radial Solution

The purpose of this paper is to investigate the existence of non-radial entire positive bounded solutions to the following semilinear elliptic system We assume that the following basic conditions hold throughout the paper.(H1) p,q:RN→[0,∞);(H2) f,g are continuous and non-decreasing on [0,∞),f(t)>0, g(t)>0,(?) t>0. Before stating our main results, we denote for r>0where and for r≥c>0where c is a positive constant, and We see that and thus H1,H2have the inverse functions H1-1，H2-1on [c,∞),respectively. Our main results are summarized as follows．Theorem2.1Under the hypotheses (H1) and (H2),if we further suppose that(H3) P1(∞)<∞;(H4) there exist positive constants a and b with a+b≥c such that H1(a+b)+P1(∞)+P2(∞)<H1(∞), then system (2.1) has infinitely many entire positive bounded、olution (u(x),v(x)) with u(x)≥α,v(x)≥b,(?)x∈RN.Theorem2.2Under the hypotheses (H1) and (H2),if we further suppose that(H5) Λ1(∞)＜∞,(H6) there exist positive constants a and b with a+b≥c such that H2(a+b+Λ1(∞)+Λ2(∞)<H2(∞)， then system (2.1) has infinitely many entire positive bounded、olution (u(x),v(x)) with u(x)≥a, v(x)≥b,(?)x∈RN.Theorem2.3Let p, q satisfy (H1)and (H3),fi,gi(i=1,2) satisfy (H2).Suppose that(H7) there exist positive constants a and b with a＋b≥c such that H01(a+b)+P1(∞)+P2(∞)<H01(∞), where then the following system has infinitely many entire positiv。bounded、olution(u(x),u(x)) with u(x)≥α,u(x)≥b,(?)x∈RN.Theorem2．4Let p, q satisfy (H1）and (H3）,f2，gi (i＝1，2) satisfy (H2).Suppos that (H8) there exist positive constants a and b with a＋b≥c such that Hoe(a+b)+Λ1(∞)+Λ2(H∞)<H02(∞), where then system(1.3)has infinitely many entire positive bounded、olution (u(x),v(x)) with u(x)≥α,u(x)≥b,(?)x∈RN．...