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Lane-Emden equation for the superposition of a local and nonlocal operator with the "wrong sign"
We consider the Lane-Emden equation associated with the operator $-Δ- γ\, (-Δ)^s$ (for positive $γ$). First we consider the equation in the entire space and we prove that no Serrin-type critical exponent arises in the $H^1(\mathbb R^n)$ framework. Secondly we consider the problem settled in an open,
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