Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on x′
Texas State University-San Marcos, Department of Mathematics
Using a fixed point theorem in cones, this paper shows the existence of positive solutions for the singular three-point boundary-value problem x″(t) + α(t)ƒ(t, x(t), x′(t)) = 0, 0 < t < 1, x′(0) = 0, x(1) = αx(η), where 0 < α < 1, 0 < η < 1, and ƒ may change sign and may be singular at x = 0 and x′ = 0.
Three-point boundary value problem, Singularity, Positive solutions, Fixed point theorem
Chen, Y., Yan, B., & Zhang, L. (2007). Positive solutions for singular three-point boundary-value problems with sign changing nonlinearities depending on x′. <i>Electronic Journal of Differential Equations, 2007</i>(63), pp. 1-9.