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Ground state solutions for singular semi-linear elliptic equations. (English) Zbl 1167.35371

Summary: We prove the existence of a ground state solution for the semi-linear elliptic equation \(-\Delta u = f(x,u)\) on \(\mathbb R^N\) under suitable conditions on a locally Hölder continuous non-linearity \(f(x,t)\). The non-linearity may exhibit a singularity as \(t\rightarrow 0^{+}\).

MSC:

35J60 Nonlinear elliptic equations
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