Osaka Journal of Mathematics

A comparison principle and applications to asymptotically $p$-linear boundary value problems

Dang Dinh Hai

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Abstract

Consider the problems \begin{equation*} \left\{ \begin{array}{@{}ll@{}} -\Delta_{p}u=f\ \text{in}\ \Omega{,} & u=0\ \text{on}\ \partial \Omega,\\ -\Delta_{p}v=g\ \text{in}\ \Omega{,} & v=0\ \text{on}\ \partial \Omega, \end{array} \right. \end{equation*} where $\Omega$ is a bounded domain in $\mathbb{R}^{n}$ with smooth boundary $\partial \Omega$, $\Delta_{p}z=\mathrm{div}(\lvert\nabla z\rvert^{p-2}\nabla z)$, $p>1$. We prove a strong comparison principle that allows $f-g$ to change sign. An application to singular asymptotically $p$-linear boundary problems is given.

Article information

Source
Osaka J. Math., Volume 52, Number 2 (2015), 393-409.

Dates
First available in Project Euclid: 24 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1427202893

Mathematical Reviews number (MathSciNet)
MR3326617

Zentralblatt MATH identifier
1325.35042

Subjects
Primary: 35J95 35J70: Degenerate elliptic equations

Citation

Hai, Dang Dinh. A comparison principle and applications to asymptotically $p$-linear boundary value problems. Osaka J. Math. 52 (2015), no. 2, 393--409. https://projecteuclid.org/euclid.ojm/1427202893


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