Periodic solution to p-Laplacian neutral Liénard type equation with variable parameter
Tóm tắt
Using Mawhin’s continuation theorem we obtain some existence results of periodic solutions for a type of p-Laplacian neutral Liénard equation
$$\left( {\phi _p \left( {\left( {x\left( t \right) - c\left( t \right)x\left( {t - \tau } \right)} \right)^\prime } \right)} \right)^\prime + f\left( {x\left( t \right)} \right)x'\left( t \right) + g\left( {x\left( {t - \gamma \left( t \right)} \right)} \right) = e\left( t \right).$$
It is worth noting that c(t) is no longer a constant which is different from the corresponding ones of past work.
Tài liệu tham khảo
LU, S.— REN, J.— GE, W.: Problems of periodic solutions for a kind of second order neutral functional differential equation, Appl. Anal. 82 (2003), 411–426.
ZHU, Y.— LU, S.: Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments, J. Math. Anal. Appl. 336 (2007), 1357–1367.
DU, B.— GUO, L.— GE, W.— LU, S.: Periodic solutions for generalized Liénard neutral equation with variable parameter, Nonlinear Anal. 70 (2009), 2387–2394.
GAINES, R.— MAWHIN, J.: Coincidence Degree and Nonlinear Differential Equations, Springer, Berlin, 1977.