Find in Library

<p/> <p>By using the fixed-point index theorem, we consider the existence of positive solutions for the following nonlinear higher-order four-point singular boundary value problem on time scales <inline-formula><graphic file="1687-1847-2009-209707-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i2.gif"/></inline-formula>; <inline-formula><graphic file="1687-1847-2009-209707-i3.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i4.gif"/></inline-formula>; <inline-formula><graphic file="1687-1847-2009-209707-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i6.gif"/></inline-formula>; <inline-formula><graphic file="1687-1847-2009-209707-i7.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i8.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2009-209707-i9.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i10.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i11.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i12.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i13.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i14.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2009-209707-i15.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2009-209707-i16.gif"/></inline-formula> is rd-continuous.</p>