Amster, Pablo; Mariani, María Cristina Two iterative schemes for an \(H\)-system. (English) Zbl 1092.34509 JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 5, 7 p. (2005). The authors consider the nonlinear boundary value problem \[ \begin{aligned} f'- f=-2H(f, g)f g',\quad x\in I,\qquad &g''= 2H(f,g)f f',\quad x\in I,\\ f(0)= \alpha_0,\quad f(L)=\alpha_L,\qquad &g(0)= \beta_0,\quad g(L)= \beta_L,\end{aligned}\tag{1} \] where \(f,g\in C^2(\overline I)\); \(f> 0\), \(g'> 0\) in \(I= (0,L)\subset \mathbb{R}\); \(H: \mathbb{R}^2\to \mathbb{R}\) is a given continuous function; and \(\alpha_0,\alpha_L> 0\), \(\beta_0< \beta_L\) are fixed real numbers.Two iterative schemes for the solution of problem (1) are studied: a Newton imbedding-type procedure, and a scheme based on the method of upper and lower solutions. Reviewer: Anatolij Ivan Kolosov (Khar’kov) MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A45 Theoretical approximation of solutions to ordinary differential equations Keywords:Newton imbedding; upper and lower solutions; iterative methods; Leray-Schauder degree theory PDFBibTeX XMLCite \textit{P. Amster} and \textit{M. C. Mariani}, JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 5, 7 p. (2005; Zbl 1092.34509) Full Text: EuDML