Cabada Fernández, AlbertoKhaldi, Rabah2024-12-032024-12-032021-06-04Cabada, A., and R. Khaldi. “Existence of Solutions of a Second Order Equation Defined on Unbounded Intervals With Integral Conditions on the Boundary”. Malaya Journal of Matematik, vol. 9, no. 03, July 2021, pp. 117-28, doi:10.26637/mjm0903/0062319-3786https://hdl.handle.net/10347/37954In this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary: \begin{equation*} u^{\prime \prime }\left( t\right) -m^{2}u\left( t\right) +f( t,e^{-mt}u\left( t\right) ,e^{-mt}\,u^{\prime }\left( t\right)) =0,\quad \mbox{for all}\;t\in % \left[ 0,+\infty \right) , \label{1.1} \end{equation*} \begin{equation*} \label{1.2} u\left( 0\right) -\frac{1}{m}u^{\prime }\left( 0\right) =\int\limits_{0}^{+\infty }e^{-2ms}u\left( s\right) ds,\underset{% t\rightarrow +\infty }{\lim }{\left\{e^{-mt}u\left( t\right) \right\}} =B, \end{equation*}% where $m>0,m\neq \frac{1}{6},B\in \mathbb{R}$ and $f:\left[ 0,+\infty \right) \times \mathbb{R}^{2}\rightarrow \mathbb{R} $ is a continuous function satisfying a suitable locally $L^1$ bounded condition and a kind of Nagumo's condition with respect to the first derivative.engCopyright (c) 2021 Alberto Cabada, Rabah KhaldiAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Boundary value problemsIntegral boundary conditionsUpper and lower solutions methodExistence of solution120219 Ecuaciones diferenciales ordinariasjournal article10.26637/mjm0903/0062321-5666open access