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Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$

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  • We prove existence of extremal functions for some Rellich-Sobolev type inequalities involving the $L^2$ norm of the Laplacian as a leading term and the $L^2$ norm of the gradient, weighted with a Hardy potential. Moreover we exhibit a breaking symmetry phenomenon when the nonlinearity has a growth close to the critical one and the singular potential increases in strength.
    Mathematics Subject Classification: 26D10, 47F05.


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