Nonresonance for a one-dimensional -Laplacian with strong singularity

In this work, we give nonresonance conditions for a singular quasilinear two-point boundary value problem { ( φ p ( u ′ ) ) ′ + h ( t ) f ( t , u ) = k ( t , u , u ′ ) , a.e. in ( 0 , 1 ) , u ( 0 ) = u ( 1 ) = 0 , where φ p ( x ) = | x | p − 2 x , p > 1 , f ∈ C ( [ 0 , 1 ] × R , R ) , h is a nonnegative measurable function on ( 0 , 1 ) , and k : ( 0 , 1 ) × R × R → R is a Carathéodory function dominated by K ∈ L 1 ( 0 , 1 ) , i.e., | k ( t , x , y ) | ≤ K ( t ) for all ( t , x , y ) ∈ ( 0 , 1 ) × R × R .