【摘要】 研究了下面带有p-Laplacian算子的非线性奇异边值系统:(p(ui′))′+ai(t)fi(u1,u2)=0,0<t<1,iαp(ui(0))-iβp(ui′(0))=0,iγp(ui(1))+iδp(ui′(1))=0,(i=1,2)正解的存在性.其中p(s)为p-Laplacian算子,即p(s)=|s|p-2s,p>1,(p)-1=q,1p+1q=1,iα>0,iβ0,iγ>0,iδ0,i=1,2.这里fi是下半连续函数(i=1,2).通过使用锥上的不动点定理,在相当弱的条件下,获得了这类奇异边值系统正解的存在性.更多还原

【Abstract】 The existence of positive solutions for a class of nonlinear singular boundary value systems with-pLaplacian is studied:(p(ui′))′+ai(t)fi(u1,u2)=0,0<t<1,iαp(ui(0))-iβp(ui′(0))=0,iγp(ui(1))+iδp(ui′(1))=0,(i=1,2) wherep(s)=|s|p-2s,p>1,(p)-1=q,1p+1 q=1,iα>0,iβ 0,iγ>0,iδ 0,i=1,2.fiare lower semi-con-tinuous functions(i=1,2).By using the fixed-point theorem of cone expansion and compression of norm type,the existence of positive solutions for a nonlinear singular boundary value system with-pLaplacian are obtained.更多还原