periodic solution

Semilinear periodic equation with arbitrary nonlinear growth and data measure: mathematical analysis and numerical simulation

In this work, we are interested in the existence, uniqueness, and numerical simulation of weak periodic solutions for some semilinear elliptic equations with data measures and with arbitrary growth of nonlinearities.  Since the data are not very regular and the growths are arbitrary, a new approach is needed to analyze these types of equations.  Finally, a suitable numerical discretization scheme is presented.  Several numerical examples are given which show the robustness of our algorithm.

Existence of periodic solution for a higher-order p-Laplacian differential equation with multiple deviating arguments

By applying Mawhin's continuation theorem, theory of Fourier series, Bernoulli numbers theory and some new inequalities, we study the higher-order $p$-Laplacian differential equation with multiple deviating arguments of the form \[(\varphi_{p}(x^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-\tau_{1}(t)),\ldots,x(t-\tau_{k}(t)))+e(t).\] Some new results on the existence of periodic solutions for the previous equation are obtained.