Fourier series and neutral functional differential equations
The authors investigate the existence and uniqueness of periodic solutions to a class of neutral differential equations with delay of the form NEWLINE\[NEWLINEx''(t)+a_1x'(t)+a_2x(t)+ cx''(t-h)+c_1x'(t-h)+c_2x(t-h)=f(t),NEWLINE\]NEWLINE where \(h\geq 0,c,a_i,c_i\;(i=1,2)\) are constants, and \(f\) is a continuous and periodic function with period \(2\pi\). Moreover, the assumption that the Fourier series for \(f\) is uniformly convergent is required. Results are obtained by using Fourier series theory and real analytic inequalities.
scientific article; zbMATH DE number 6058730
scientific article