Positive solutions to semi-positone second-order three-point problems on time scales

Using a fixed point theorem of generalized cone expansion and compression we establish the existence of at least two positive solutions for the nonlinear semi-positone three-point boundary value problem on time scales u^@D^@?(t)[email protected](t,u(t))=0,u(a)=0,@au(@h)=u(T). Here [email protected]?[a,T]"T, where T is a time scale, @a>0,@[email protected]?(a,@r(T))"T,@a(@h-a)0 belongs to a certain interval. These results are new for difference equations as well as for general time scales. An example is provided for differential, difference, and q-difference equations.

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