Open AccessTHE FAMILY OF FUNCTIONS $S_{\alpha, k}$ AND THE LIENARD EQUATION
Author(s) -
Hamilton Luiz GUIDORlZZI
Publication year - 1996
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.27.1996.4368
Subject(s) - int , mathematics , alpha (finance) , combinatorics , statistics , computer science , construct validity , psychometrics , operating system
In this paper we study qualitatively the Lienard Equation $\ddot x+f(x)\dot x+g(x)=0$ with aid of the non-usual family of funct10ns given by
\[ S_{\alpha, k}(x, y)=\int^{y+F(x)-\alpha G(x)-k}_0 \frac{s}{\alpha s+1} ds +\int_0^x g(u) du\]
where$F(x)=\int_0^x f(u) du$, $G(x)=\int_0^x g(u) du$ and $\alpha, k\in R$.