Advances in Pure and Applied Mathematics
, Volume 10 (4): 12 – Oct 1, 2019

/lp/de-gruyter/existence-of-positive-solutions-for-a-neumann-boundary-value-problem-dl8hBv9n2K

- Publisher
- de Gruyter
- Copyright
- © 2019 Walter de Gruyter GmbH, Berlin/Boston
- ISSN
- 1869-6090
- eISSN
- 1869-6090
- DOI
- 10.1515/apam-2018-0087
- Publisher site
- See Article on Publisher Site

AbstractIn 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)𝑑x=1{\int_{0}^{+\infty}q(x)\,dx=1} and f:ℝ+×ℝ2→ℝ{f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory.

Advances in Pure and Applied Mathematics – de Gruyter

**Published: ** Oct 1, 2019

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