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

E. I. Abduragimov

Daghestan Electronic Mathematical Reports, Tome 11 (2019), pp. 28-48

Résumé

A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $0$, $y(0)=y(1)=0$ 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.

Détail

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