Abstract
In this paper, we establish existence of solutions for the following boundary value problem on the half-line: \((q(t)u''(t))' = g(t, u(t), u'(t), u''(t)),\;\;\; t \in (0, \infty )\) subject to the boundary conditions \( u'(0) = \sum ^{m}_{i=1}\alpha _i\int ^{\xi _i}_0 u(t)\mathrm{d}t, u(0) = 0,\; \lim _{t\rightarrow \infty }q(t)u''(t)=0.\) We establish sufficient conditions for the existence of at least one solution using coincidence degree arguments. An example is provided to validate our result.
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The author wishes to express his gratitude to the anonymous referees for their useful suggestions and corrections.
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Iyase, S.A. On a third-order boundary value problem at resonance on the half-line. Arab. J. Math. 8, 43–53 (2019). https://doi.org/10.1007/s40065-018-0209-5
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DOI: https://doi.org/10.1007/s40065-018-0209-5