The main objective of the paper is to give the specific forms of the meromorphic solutions of the equation
$f^{n}(z)f(z+c)+P_{d}(z,f)=p_{1}(z)e^{\alpha_{1}(z)}+p_{2}(z)e^{\alpha_{2}(z)}$,
where $c\in \mathbb{C}\setminus\{0\}$, $P_d(z,f)$ is a differential-difference polynomial in $f$ of degree $d\leq n-1$ with small functions of $f$ as its coefficients, $p_1, p_2(\not\equiv 0)$ are rational functions and $\alpha_1$, $\alpha_2$ are non-constant polynomials.
This paper is concerned with a system of magnetic effected piezoelectric beams with distributed delay term, where the heat flux is given by Cattaneo’s law (second sound). We prove the existence and the uniqueness of the solution using the semigroup theory. Then, we establish the exponential stability of the solution by introducing a suitable Lyapunov functional.
