%0 Journal Article %1 0951-7715-27-3-563 %A Llibre, Jaume %A Novaes, Douglas D %A Teixeira, Marco A %D 2014 %J Nonlinearity %K myown published top %N 3 %P 563 %T Higher order averaging theory for finding periodic solutions via Brouwer degree %U http://stacks.iop.org/0951-7715/27/i=3/a=563 %V 27 %X In this paper we deal with nonlinear differential systems of the form ##IMG## http://ej.iop.org/images/0951-7715/27/3/563/non465661ueqn001.gif equation*x'(t)=\sum_i=0^k\varepsilon^i F_i(t,x)+\varepsilon^k+1 R(t,x,\varepsilon), equation* where ##IMG## http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn001.gif $F_i:RD\rightarrowR^n$ for i = 0, 1, …, k , and ##IMG## http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn002.gif $R:RD\times(-\varepsilon_0,\varepsilon_0)\rightarrowR^n$ are continuous functions, and T -periodic in the first variable, D being an open subset of ##IMG## http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn003.gif $R^n$ , and ε a small parameter. For such differential systems, which do not need to be of class ##IMG## http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn004.gif $C^1$ , under convenient assumptions we extend the averaging theory for computing their periodic solutions to k -th order in ε . Some applications are also performed.

@article{0951-7715-27-3-563, abstract = {In this paper we deal with nonlinear differential systems of the form ##IMG## [http://ej.iop.org/images/0951-7715/27/3/563/non465661ueqn001.gif] {\begin{equation*}x'(t)=\sum_{i=0}^k\varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon), \end{equation*} } where ##IMG## [http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn001.gif] {$F_i:\mathbb{R}\times D\rightarrow\mathbb{R}^n$} for i = 0, 1, …, k , and ##IMG## [http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn002.gif] {$R:\mathbb{R}\times D\times(-\varepsilon_0,\varepsilon_0)\rightarrow\mathbb{R}^n$} are continuous functions, and T -periodic in the first variable, D being an open subset of ##IMG## [http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn003.gif] {$\mathbb{R}^n$} , and ε a small parameter. For such differential systems, which do not need to be of class ##IMG## [http://ej.iop.org/images/0951-7715/27/3/563/non465661ieqn004.gif] {$\mathcal{C}^1$} , under convenient assumptions we extend the averaging theory for computing their periodic solutions to k -th order in ε . Some applications are also performed.}, added-at = {2015-12-28T05:56:12.000+0100}, author = {Llibre, Jaume and Novaes, Douglas D and Teixeira, Marco A}, biburl = {https://www.bibsonomy.org/bibtex/23424041dcaa17218826fad0a5fccc14a/ddnovaes}, interhash = {6072734ed29afa7d80376256ac2482f5}, intrahash = {3424041dcaa17218826fad0a5fccc14a}, journal = {Nonlinearity}, keywords = {myown published top}, number = 3, pages = 563, timestamp = {2015-12-28T16:50:10.000+0100}, title = {Higher order averaging theory for finding periodic solutions via Brouwer degree}, url = {http://stacks.iop.org/0951-7715/27/i=3/a=563}, volume = 27, year = 2014 }