%0 Journal Article
%T Positive Solutions to Nonlinear First-Order Nonlocal BVPs with Parameter on Time Scales
%A Chenghua Gao
%A Hua Luo
%J Boundary Value Problems
%D 2011
%I Springer
%R 10.1155/2011/198598
%X We discuss the existence of solutions for the first-order multipoint BVPs on time scale   : u¦¤(t)+p(t)u(¦Ò(t))=¦Ëf(t,u(¦Ò(t))), t¡Ê[0,T]  , u(0)-¡Æi=1m¦Áiu(¦Îi)=0, where ¦Ë>0 is a parameter, T>0 is a fixed number, 0,T¡Ê  , f:[0,T]  ¡Á[0,¡Þ)¡ú[0,¡Þ) is continuous, p is regressive and rd-continuous, ¦Ái¡Ý0, ¦Îi¡Ê  , i=1,2,¡­,m, 0=¦Î0<¦Î1<¦Î2< <¦Îm-1<¦Îm=¦Ò(T), and 1-¡Æi=1m(¦Ái/ep(¦Îi,0))>0. For suitable ¦Ë>0, some existence, multiplicity, and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index.
%U http://dx.doi.org/10.1155/2011/198598