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- W2905827246 abstract "We consider a class of weighted Emden-Fowler equations begin{equation} tag{$mathcal P_{alpha}$} label{eqab} left{begin{array}{ll} -Delta u=V_{alpha} (x) , u^p & text{in} ,,B, u>0 & text{in} ,,B, u=0 & text{on},,partial B, end{array}right. end{equation} posed on the unit ball $B=B(0,1)subset mathbb R^N$, $N geq1$. We prove that symmetry breaking occurs for the groundstate solutions as the parameter $alpha rightarrow infty.$ The above problem reads as a possibly large perturbation of the classical H'enon equation. We consider a radial function $V_alpha$ having a spherical shell of zeroes at $|x|=R in (0,1].$ For $N geq 3$, a quantitative condition on $R$ for this phenomenon to occur is given by means of universal constants, such as the best constant for the subcritical Sobolev's embedding $H^1_0(B)subset L^{p+1}(B).$ In the case $N=2$ we highlight a similar phenomenon when $R=R(alpha)$ is a function with a suitable decay. Moreover, combining energy estimates and Liouville type theorems we study some qualitative and quantitative properties of the groundstate solutions to (ref{eqab}) as $alpha rightarrow infty.$" @default.
- W2905827246 created "2019-01-01" @default.
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- W2905827246 date "2019-10-09" @default.
- W2905827246 modified "2023-10-06" @default.
- W2905827246 title "Quantitative symmetry breaking of groundstates for a class of weighted Emden–Fowler equations" @default.
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- W2905827246 doi "https://doi.org/10.1088/1361-6544/ab2d6f" @default.
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