Periodic boundary value problems for $n$th-order ordinary differential equations with $p$-laplacian

Liu, Yuji; Ge, Weigao

Liu, Yuji ; Ge, Weigao

J. Appl. Math., Tome 2005 (2005) no. 1, p. 1-21 / Harvested from Project Euclid

Résumé

We prove existence results for solutions of periodic boundary value problems concerning the $n$ th-order differential equation with $p$ -Laplacian $[\phi (x^{(n-1)}(t))]' = f(t, x(t), x'(t), \dotsc,\linebreak x^{(n-1)}(t))$ and the boundary value conditions $x^{(i)}(0)\!=\! x^{(i)}(T)$ , $i= 0, \dotsc, n-1$ . Our method is based upon the coincidence degree theory of Mawhin. It is interesting that $f$ may be a polynomial and the degree of some variables among $x_0, x_1, \dotsc, x_{n-1}$ in the function $f(t, x_0, x_1, \dotsc, x_{n-1})$ is allowed to be greater than $1$ .

Publié le : 2005-02-16
Classification:

@article{1113922281,
     author = {Liu, Yuji and Ge, Weigao},
     title = {Periodic boundary value problems for $n$th-order ordinary differential equations with $p$-laplacian},
     journal = {J. Appl. Math.},
     volume = {2005},
     number = {1},
     year = {2005},
     pages = { 1-21},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1113922281}
}

Liu, Yuji; Ge, Weigao. Periodic boundary value problems for $n$th-order ordinary differential equations with $p$-laplacian. J. Appl. Math., Tome 2005 (2005) no. 1, pp.  1-21. http://gdmltest.u-ga.fr/item/1113922281/