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 $a_0{x}^{\gamma }{y}^p\le f(x,y)\le a_1{y}^p$, where $a_0>0$, $a_1>0$, $p>1$, $\gamma \ge 0$ – constants.

Détail

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

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