Multiple positive solutions of nonlinear third-order BVP for a class of p-Laplacian dynamic equations on time scales

In this paper, by using fixed-point theorems in cones, the existence of multiple positive solutions is considered for singular nonlinear boundary value problem for the following third-order p-Laplacian dynamic equations on time scales (@F"p(u^@D^@D(t)))^@?+f(t,u(t))=0,t@?[a,b],@au(@r(a))-@bu^@D(@r(a))=0,@cu(b)+@du^@D(b)=0,u^@D^@D(@r(a))=0, where @F"p(s) is p-Laplacian operator, i.e., @F"p(s)=|s|^p^-^2s,p>1,@F"p^-^1=@F"q,1p+1q=1. In particular, the conditions we used in the paper are different from those in [R.Y. Ma, Existence of solutions of nonlinear m-point boundary value problem, J. Math. Anal. Appl. 256 (2001) 556-567; A.M. Mao, S.X. Luan, Y.H. Ding, On the existence of positive solutions for a class of singular boundary value problems, J. Math. Appl. 298 (2004) 57-72].

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