### Approximation theory

### Daghestan Electronic Mathematical Reports: Issue 11 (2019)

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

### UDK: 517.946

### Pages: 38 - 48

### DOI: 10.31029/demr.11.5

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.

**Keywords: **
positive solution, a priori estimates, differential equation, two-point boundary value problem.