The Study Of Existence And Multiplicity Of Positive Solutions For Dynamic Equations BVP On Measure Chains

The theory of dynamic equations on measure chains,introduced in 1988 by Stefan Hilger , unifies and extends continuous and discrete analysis and also provides a framework for studying general class of dynamic equations. This is not only because it can provide a unifying structure for the study of differential equations in the continuous case and the study of finite difference equations in the discrete case, but also because the study of measure chains has led to many important applications. The boundary problems for dynamic equations on measure chains arise in a variety of different areas of applied mathematics and physics hence, they have received much attention.We study the related properties of Nabla exponential function and three classes of boundary value problems of dynamic eqations on measure chains are investigated in this paper. By means of the fixed theorem of cone expansion and compression, fixed point index, techniques of transformations on measure chains and so on, some existence and multiplicity results for positive solutios of BVP on measure chains are obtained. Our criteria generalize and improve some kown results.