The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying...The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.展开更多
In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient condit...In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient conditions are established. In particular, for the alm ost periodic system , the existence of strictly positive alm ostperiodic solutions is obtained. Som e previous results are im proved and generalized.展开更多
A diode laser array(DLA)positioned in an external cavity can receive the radiations emitted from its neighboring elements (C 1) and that of itself (S) after being reflected at the DLA facet as well as from the externa...A diode laser array(DLA)positioned in an external cavity can receive the radiations emitted from its neighboring elements (C 1) and that of itself (S) after being reflected at the DLA facet as well as from the external mirror (C 0). Considering the fact that｜C 0/S｜ should be larger than unity if the external cavity is effective,and｜C 1/S｜ should be larger than unity if the phase locking may be established in the external cavity.The requirements on the reflection at the facet of the diode laser array have been specified in terms of the cavity length and reflection coefficient of the external mirror.展开更多
基金Natural Scince Foundation of China and Foundation for University Key Teacher by the Ministry of Education
文摘The existence of positive solutions for second order m-point boundary value problemx″-q(t)f(x,x′)x′=0, x(0)= m i=2 b ix(ξ i),x′(1)=αx′(0)are investigated,where ξ i,b i and α are constants satisfying 0=ξ 1<ξ 2<...<ξ m-1 <ξ m=1,b i≥0 for i=2,...,m with β∶= m i=2 b i∈[0,1), and α>1. Our approach is based on the fixed point theorem in cones.
文摘In this paper, the existence of strictly positive solutions for N-species nonau- tonom ous Kolm ogorov com petition system s is studied. By applying the Schauder's fixed point theorem som e new sufficient conditions are established. In particular, for the alm ost periodic system , the existence of strictly positive alm ostperiodic solutions is obtained. Som e previous results are im proved and generalized.
文摘A diode laser array(DLA)positioned in an external cavity can receive the radiations emitted from its neighboring elements (C 1) and that of itself (S) after being reflected at the DLA facet as well as from the external mirror (C 0). Considering the fact that｜C 0/S｜ should be larger than unity if the external cavity is effective,and｜C 1/S｜ should be larger than unity if the phase locking may be established in the external cavity.The requirements on the reflection at the facet of the diode laser array have been specified in terms of the cavity length and reflection coefficient of the external mirror.
