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Infinitely many radial solutions of a non--homogeneous $p$--Laplacian problem

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  • In this paper we investigate the existence of infinitely many radial solutions for the elliptic Dirichlet problem \[ \left\{ \begin{array}{ll} \displaystyle{-\Delta_p u\ =|u|^{q-2}u + f(x)} & \mbox{ in } B_R,\\ \displaystyle{u=\xi} & \mbox{ on } \partial B_R,\\ \end{array} \right. \] where $B_R$ is the open ball centered in $0$ with radius $R$ in $\mathbb{R}^N$ ($N \geq 3$), $2 < p < N$, $p< q < p^*$ (with $p^* = \frac{pN}{N-p}$), $\xi\in\mathbb{R}$ and $f$ is a continuous radial function in $\overline B_R$. The lack of even symmetry for the related functional is overcome by using some perturbative methods and the radial assumptions allow us to improve some previous results.
    Mathematics Subject Classification: Primary: 35J92; Secondary: 35J60, 35J66, 58E05.


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