Periodic solutions for a Rayleigh type p-Laplacian equation with sign-variable coefficient of nonlinear term
By using Lu's continuation theorem, which is an extension of a result of Manásevich-Mawhin, the authors study the existence of periodic solutions for the Rayleigh type \(p\)-Laplacian equation \[ (\varphi _p(x^{\prime}(t)))^{\prime}+f(x^{\prime}(t))+g_{1}(x(t-\tau _{1}(t,|x|_{\infty })))+\beta (t)g_{2}(x(t-\tau _{2}(t,|x|_{\infty })))=e(t). \] This paper includes the case that the growth order with respect to the variable \(u\) in \(g_1(u)\) is allowed to be greater than \(p-1\) and the coefficient \(\beta (t)\) of \(g_2(x(t-\tau _2(t, |x|_{\infty })))\) can change sign.
scientific article; zbMATH DE number 5726768
scientific article