An iterative method of solving a boundary-value problem for a nonlinear differential equation with a deflected argument

1976 ◽  
Vol 27 (5) ◽  
pp. 527-532
Author(s):  
I. V. Brich
Keyword(s):  
Differential Equation ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Nonlinear Differential Equation ◽  
Boundary Value

A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation

2019 ◽  
pp. 38-48
Author(s):  
Edelkhan Abduragimov
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Nonlinear Differential Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Second Order ◽  
Point Boundary ◽  
Priori Estimates

A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \in [0,1]$, $y \in R$ and satisfies the condition $a_0 x^{\gamma}y^p \leq f(x,y) \leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\gamma \geq 0$ -- constants.

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