Existence and boundary behavior of solutions for boundary blow-up quasilinear elliptic problems with gradient terms

Abstract

. In this paper, by sub-supersolution methods, Karamata regular variation theory and perturbation method, we study the existence, uniqueness and asymptotic behavior of solutions near the boundary to quasilinear elliptic problem where Ω is a bounded domain with smooth boundary in R N ( N (cid:2) 2 ) , 1 < m (cid:3) 2, 0 < q (cid:3) m / ( m − 1 ) . b ∈ C α ( Ω )( α ∈ ( 0 , 1 )) is positive in Ω , and may be vanishing on the boundary, and f ∈ C 1 [ 0 , + ∞ ) , f ( 0 ) = 0, is increase on ( 0 , + ∞ ) and normalized regularly varying at in fi nity with positive index p and p +( q − 1 )( m − 1 ) > 0.