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Summary:
Existence results are established for the resonant problem $y^{\prime \prime }+\lambda _m \,a\,y=f(t,y)$ a.e. on $[0,1]$ with $y$ satisfying Dirichlet boundary conditions. The problem is singular since $f$ is a Carathéodory function, $a\in L_{{\mathrm loc}}^1(0,1)$ with $a>0$ a.e. on $[0,1]$ and $\int ^1_0 x(1-x)a(x)\,\mathrm{d}x <\infty $.
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