The paper claims existence of positive radial solutions for the mixed Laplacian-fractional Laplacian Lane-Emden equation at exponents slightly below the local critical exponent, implying the whole-space critical exponent is smaller than the bounded-domain one.
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Mixed local and nonlocal laplacian without standard critical exponent for Lane-Emden equation
The paper claims existence of positive radial solutions for the mixed Laplacian-fractional Laplacian Lane-Emden equation at exponents slightly below the local critical exponent, implying the whole-space critical exponent is smaller than the bounded-domain one.