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Strong comparison and strong maximum principles for quasilinear elliptic equations with a gradient term

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Abstract

In this paper, we prove strong comparison principles for the quasilinear elliptic equation

$$\begin{aligned} -\Delta _p u + a(u) |\nabla u|^q = f(u), \quad u>0 \quad \text { in } \Omega , \end{aligned}$$

where \(\frac{2N+2}{N+2}< p < 2\), \(q\ge 1\), \(\Omega \) is a bounded domain of \(\mathbb {R}^N\) and a, f satisfy some relevant conditions. We also prove a strong maximum principle for the corresponding linearized equation.

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Funding

This research is funded by University of Economics and Law, Vietnam National University, Ho Chi Minh City, Vietnam.

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  1. Faculty of Economic Mathematics, University of Economics and Law, Ho Chi Minh City, Vietnam

    Phuong Le

  2. Vietnam National University, Ho Chi Minh City, Vietnam

    Phuong Le

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Le, P. Strong comparison and strong maximum principles for quasilinear elliptic equations with a gradient term. Positivity 27, 55 (2023). https://doi.org/10.1007/s11117-023-01006-3

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