On the solvability of a resonant third-order integral \(m\)-point boundary value problem on the half-line (Q2664887)

Summary: 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 \(\left( \rho \left( t\right) u^\prime \left( t\right)\right)''=w\left( t, u \left( t\right), u^\prime \left( t\right), u'' \left( t\right)\right),t\in\left[ 0, \infty\right),u\left( 0\right)= \sum_{j = 1}^m \alpha_j \int_0^{\eta_j}u\left( t\right)dt, u^\prime\left( 0\right)=0, \lim_{t \longrightarrow \infty} \left( \rho \left( t\right) u^\prime \left( t\right)\right)^\prime=0\), 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.