The exact boundary behavior of solutions to singular nonlinear Lane–Emden–Fowler type boundary value problems. (February 2015) - Zhang, Zhijun; Li, Bo; Li, Xiaohong
Abstract: In this paper we analyze the exact boundary behavior of solutions to singular nonlinear Dirichlet problems − △ u = b ( x ) g ( u ) + λ a ( x ) f ( u ), u > 0, x ∈ Ω, u | ∂ Ω = 0, where Ω is a bounded domain with smooth boundary in R N, λ ≥ 0, g ∈ C 1 ( ( 0, ∞ ), ( 0, ∞ ) ), lim s → 0 + g ( s ) = ∞, b, a ∈ C loc α ( Ω ), are positive in Ω, may be vanishing or singular on the boundary, and f ∈ C ( [ 0, ∞ ), [ 0, ∞ ) ) . We reveal that the nonlinear term λ a ( x ) f ( u ) does not affect the first expansion of the classical solutions near the boundary to the problem for several kinds of functions a and b .