On the Solvability of a Resonant Third-Order Integral m-Point Boundary Value Problem on the Half-Line

Abstract

In this work, the existence of at least one solution for the following third-order integral and $m$ -point boundary value problem on the half-line at resonance ${\left(\rho \left(t\right)u^{\prime }\left(t\right)\right)}^{″}=w\left(t,u\left(t\right),u^{\prime }\left(t\right),u^{″}\left(t\right)\right),t\in \left[0,\infty \right),u\left(0\right)={\sum }_{j=1}^m{\alpha }_j{\int }_0^{{\eta }_j}u\left(t\right)dt,u^{\prime }\left(0\right)=0,\underset{t⟶\infty }{\lim }{\left(\rho \left(t\right)u^{\prime }\left(t\right)\right)}^{\prime }=0,$ will be investigated. The Mawhin’s coincidence degree theory will be used to obtain existence results while an example will be used to validate the result obatined.