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Existence of positive solutions for a Neumann boundary value problem on the half-line via coincidence degree

Authors
  • Djafri, S.
  • Moussaoui, Toufik
Type
Published Article
Journal
Advances in Pure and Applied Mathematics
Publisher
De Gruyter
Publication Date
Dec 05, 2018
Volume
10
Issue
4
Pages
447–458
Identifiers
DOI: 10.1515/apam-2018-0087
Source
De Gruyter
Keywords
License
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Abstract

In this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line: { - u ′′ ⁢ ( x ) = q ⁢ ( x ) ⁢ f ⁢ ( x , u , u ′ ) , x ∈ ( 0 , + ∞ ) , u ′ ⁢ ( 0 ) = u ′ ⁢ ( + ∞ ) = 0 , \left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle u^{\prime}(0)&\displaystyle=u^{\prime}(+\infty)=0,\end{aligned}\right. where q : ℝ + → ℝ + {q:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}} is a positive measurable function such that ∫ 0 + ∞ q ⁢ ( x ) ⁢ 𝑑 x = 1 {\int_{0}^{+\infty}q(x)\,dx=1} and f : ℝ + × ℝ 2 → ℝ {f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory.

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