Geodesic
On a Numerical Method for Constructing a Positive Solution of the Two-Point Boundary-Value Problem for a Second-Order Nonlinear Differential Equation
Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 803-812

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An iterative method is proposed for finding an approximation to the positive solution of the two-point boundary-value problem $$ y''+c(x)y^m=0,\quad 01,\qquad y(0)=y(1)=0, $$ where $m=\mathrm{const}>1$ and $c(x)$ is a continuous nonnegative function on $[0,1]$. The convergence of this method is proved. An error estimate is also obtained.
Keywords: second-order nonlinear differential equation, two-point boundary-value problem, elliptic differential equation, Cauchy problem, Green function. 
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     author = {E. I. Abduragimov},
     title = {On a {Numerical} {Method} for {Constructing} a {Positive} {Solution} of the {Two-Point} {Boundary-Value} {Problem} for a {Second-Order} {Nonlinear} {Differential} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--812},
     publisher = {mathdoc},
     volume = {91},
     number = {6},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a0/}
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E. I. Abduragimov. On a Numerical Method for Constructing a Positive Solution of the Two-Point Boundary-Value Problem for a Second-Order Nonlinear Differential Equation. Matematičeskie zametki, Tome 91 (2012) no. 6, pp. 803-812. http://geodesic.mathdoc.fr/item/MZM_2012_91_6_a0/