RT Journal Article
T1 Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary
A1 Cabada Fernández, Alberto
A1 Khaldi, Rabah
K1 Boundary value problems
K1 Integral boundary conditions
K1 Upper and lower solutions method
K1 Existence of solution
AB In 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.
PB Malaya Journal of Matematik
SN 2319-3786
YR 2021
FD 2021-06-04
LK https://hdl.handle.net/10347/37954
UL https://hdl.handle.net/10347/37954
LA eng
NO Cabada, 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/mjm0903/006
NO Xunta de Galicia (Spain), project EM2014/032
DS Minerva
RD 28 abr 2026