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

Rossella Bartolo; Anna Maria Candela; Addolorata Salvatore

doi:10.3934/proc.2013.2013.51

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2013, Volume 2013: 51-59. Doi: 10.3934/proc.2013.2013.51 open access

This issue Previous Article Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains Next Article R&d dynamics

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

1.
Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Via E. Orabona 4, 70125 Bari
2.
Dipartimento di Matematica, Università degli Studi di Bari "Aldo Moro", Via E. Orabona 4, 70125 Bari

Received: August 31, 2012

Published: October 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 35J92; Secondary: 35J60, 35J66, 58E05.

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