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:RNā'[0,ā);(H2) f,g are continuous and non-decreasing on [0,ā),f(t)>0, g(t)>0,(?) t>0. Before stating our main results, we denote for r>0where and for rā„c>0where c is a positive constant, and We see that and thus H1,H2have the inverse functions H1-1ļ¼H2-1on [c,ā),respectively. Our main results are summarized as followsļ¼Theorem2.1Under the hypotheses (H1) and (H2),if we further suppose that(H3) P1(ā)<ā;(H4) there exist positive constants a and b with a+bā„c such that H1(a+b)+P1(ā)+P2(ā)<H1(ā), then system (2.1) has infinitely many entire positive boundedćolution (u(x),v(x)) with u(x)ā„Ī±,v(x)ā„b,(?)xāRN.Theorem2.2Under the hypotheses (H1) and (H2),if we further suppose that(H5) Ī1(ā)ļ¼ā,(H6) there exist positive constants a and b with a+bā„c such that H2(a+b+Ī1(ā)+Ī2(ā)<H2(ā)ļ¼ then system (2.1) has infinitely many entire positive boundedćolution (u(x),v(x)) with u(x)ā„a, v(x)ā„b,(?)xāRN.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 aļ¼bā„c such that H01(a+b)+P1(ā)+P2(ā)<H01(ā), where then the following system has infinitely many entire positivćboundedćolution(u(x),u(x)) with u(x)ā„Ī±,u(x)ā„b,(?)xāRN.Theorem2ļ¼4Let p, q satisfy (H1ļ¼and (H3ļ¼,f2ļ¼gi (iļ¼1ļ¼2) satisfy (H2).Suppos that (H8) there exist positive constants a and b with aļ¼bā„c such that Hoe(a+b)+Ī1(ā)+Ī2(Hā)<H02(ā), where then system(1.3)has infinitely many entire positive boundedćolution (u(x),v(x)) with u(x)ā„Ī±,u(x)ā„b,(?)xāRNļ¼... |