LAUSR

In this paper, we establish existence of solutions for the following boundary value problem on the half-line: $$(q(t)u''(t))' = g(t, u(t), u'(t), u''(t)),\;\;\; t \in (0, \infty )$$(q(t)u′′(t))′=g(t,u(t),u′(t),u′′(t)),t∈(0,∞) subject to the boundary conditions $$ u'(0) = \sum ^{m}_{i=1}\alpha _i\int ^{\xi _i}_0 u(t)\mathrm{d}t, u(0) = 0,\; \lim _{t\rightarrow \infty }q(t)u''(t)=0.$$u′(0)=∑i=1mαi∫0ξiu(t)dt,u(0)=0,limt→∞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.