Multiple positive solutions for p-Laplacian m-point boundary value problems on time scales

Let T be a time scale such that 0,[email protected]?T, a"i>=0 for i=1,...,m-2. Let @x"i satisfy 0<@x"1<@x"2<...<@x"m"-"2<@r(T) and @?"i"="1^m^-^2a"i<1. We consider the following p-Laplacian m-point boundary value problem on time scales(@f"p(u^@D(t)))^@?+a(t)f(t,u(t))=0,[email protected]?(0,T),u(0)=0,@f"p(u^@D(T))[email protected]?i=1m-2a"[email protected]"p(u^@D(@x"i)),where [email protected]?C"l"d((0,T),[0,~)) and [email protected]?C"l"d((0,T)x[0,~),[0,~)). Some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems respectively. In particular, our criteria extend and improve some known results.

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