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Physical Sciences and Mathematics Commons™
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Missouri University of Science and Technology
Mathematics and Statistics Faculty Research & Creative Works
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Full-Text Articles in Physical Sciences and Mathematics
Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Double Integral Calculus Of Variations On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
We consider a version of the double integral calculus of variations on time scales, which includes as special cases the classical two-variable calculus of variations and the discrete two-variable calculus of variations. Necessary and sufficient conditions for a local extremum are established, among them an analogue of the Euler-Lagrange equation.
The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner
The Convolution On Time Scales, Gusein Sh. Guseinov, Martin Bohner
Mathematics and Statistics Faculty Research & Creative Works
The main theme in this paper is an initial value problem containing a dynamic version of the transport equation. via this problem, the delay (or shift) of a function defined on a time scale is introduced, and the delay in turn is used to introduce the convolution of two functions defined on the time scale. In this paper, we give some elementary properties of the delay and of the convolution and we also prove the convolution theorem. Our investigation contains a study of the initial value problem under consideration as well as some results about power series on time scales. …