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This paper concerns the existence and multiplicity of positive solutions to the nonresonant second-order boundary-value problem $$ Lx=lambda w(t)f(t,x). $$ We are interested in the operator $Lx:=-x''+ ho qx$ when $w$ is in $L^{p}$ for $1leq p leq +infty$. Our arguments are based on fixed point theorems in a cone and Holder's inequality. The nonexistence of positive solutions is also studied.