Some recent results on the Dirichlet problem for $(p, q)$-Laplace equations

Salvatore A. Marano; Sunra J. N. Mosconi

doi:10.3934/dcdss.2018015

Article Contents

2018, Volume 11, Issue 2: 279-291. Doi: 10.3934/dcdss.2018015

This issue Previous Article Positive subharmonic solutions to superlinear ODEs with indefinite weight Next Article Location of Nodal solutions for quasilinear elliptic equations with gradient dependence

Some recent results on the Dirichlet problem for $(p, q)$-Laplace equations

Salvatore A. Marano^, and
Sunra J. N. Mosconi

Dipartimento di Matematica e Informatica, Università degli Studi di Catania, Viale A. Doria 6,95125 Catania, Italy

* Corresponding author
* Corresponding author

Received: February 2017

Revised: May 2017

Published: April 2018

Work performed under the auspices of GNAMPA of INDAM.

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Abstract

A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p, q)$-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are briefly discussed. Special attention is paid to possibly coercive, resonant, subcritical, critical, or asymmetric right-hand sides.

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Mathematics Subject Classification: Primary: 35J20, 35J92; Secondary: 58E05.

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Figure 1. Given $t\in \mathbb{R}$, on the thick part of the line $\alpha-\beta=t$ we have existence and on the dashed part non-existence of a positive eigenfunction

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