Nonresonance for a one-dimensional pp-Laplacian with strong singularity

In this work, we give nonresonance conditions for a singular quasilinear two-point boundary value problem {(φp(u′))′+h(t)f(t,u)=k(t,u,u′),a.e. in(0,1),u(0)=u(1)=0, where φp(x)=|x|p−2x,p>1φp(x)=|x|p−2x,p>1,f∈C([0,1]×R,R)f∈C([0,1]×R,R),hh is a nonnegative measurable function on (0,1)(0,1), and k:(0,1)×R×R→Rk:(0,1)×R×R→R is a Carathéodory function dominated by K∈L1(0,1)K∈L1(0,1), i.e., |k(t,x,y)|≤K(t)|k(t,x,y)|≤K(t) for all (t,x,y)∈(0,1)×R×R(t,x,y)∈(0,1)×R×R.