Dual exponential polynomials and linear differential equations
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CitationWena Zhi-Tao. Gundersen Gary G. Heittokangas Janne. (2017). Dual exponential polynomials and linear differential equations. Journal of Differential Equations, 2018; 264 (1) , 98-114. 10.1016/j.jde.2017.09.003.
We study linear differential equations with exponential polynomial coefficients, where exactly one coefficient is of order greater than all the others. The main result shows that a nontrivial exponential polynomial solution of such an equation has a certain dual relationship with the maximum order coefficient. Several examples illustrate our results and exhibit possibilities that can occur.