In this paper we study existence, uniqueness, nonexistence and asymptotic behavior of solutions to the following class of elliptic problems with strongly singular nonlinearities \(\begin{aligned} \left\{ \begin{aligned} -&\Delta u -\frac{1}{2}\left( x\cdot \nabla u\right) =\lambda u + h(x)u^{-\alpha } \quad \text{ in }\quad \mathbb {R}^{N},\\ u&>0 \quad \text{ in }\quad \mathbb {R}^{N}\text{, } \ \ u(x)\rightarrow 0 \quad \text{ as }\quad |x|\rightarrow \infty , \end{aligned} \right. \end{aligned}\) where \(N\ge 3,\) \(\lambda \in \mathbb {R}\) and \(\alpha >1\) is a real parameter and \(h: \mathbb {R}^N\rightarrow \mathbb {R}\) is a measurable function. With respect to singular problems, the novelty of this paper is that the condition \(h \in L^1\) is not imposed, unlike in most related works. By employing an auxiliary set \(\mathcal {M}\) (which contains the Nehari manifold \(\mathcal {N}\) ) together with the fibering map, we prove that the functional associated with the problem admits a minimizer u on \(\mathcal {N}\) . The properties of u and \(\mathcal {N}\) are then exploited to control the singular term and show that u is solution of the problem.
