Revistes Catalanes amb Accés Obert (RACO)

A note on nonexistence of radial solutions to semilinear elliptic inequations

M. Guedda

Resum


We study the nonexistence result of radial solutions to $-\Delta u + c\displaystyle\frac{u}{\vert x\vert^2} +\vert x\vert^\sigma \vert u\vert^qu \leq 0 $ posed in $B$ or in $ B\setminus\{0\} $ where $B$ is the unit ball centered at the origin in $\mathbb{R}^N$, $N \geq 3$. Moreover, we give a complete classification of radial solutions to the problem $-\Delta u +\displaystyle c\frac{u}{\vert x\vert^2} + \vert x\vert^\sigma \vert u\vert^qu = 0$. In particular we prove that the latter has exactly one family of radial solutions.

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