Osaka Journal of Mathematics

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

Dang Dinh Hai

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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

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

First available in Project Euclid: 24 March 2015

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Zentralblatt MATH identifier

Primary: 35J95 35J70: Degenerate elliptic equations


Hai, Dang Dinh. A comparison principle and applications to asymptotically $p$-linear boundary value problems. Osaka J. Math. 52 (2015), no. 2, 393--409.

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