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

Existence of positive solutions for a Neumann boundary value problem on the half-line via... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

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

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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

Abstract

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.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Oct 1, 2019

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