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arXiv · 2203.11477

Strong comparison principle for a p-Laplace equation involving singularity and its applications

R. Dhanya·M. S. Indulekha·Ritabrata Jana
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Abstract

In this paper we prove a strong comparison principle for radially decreasing solutions $u,v\in C_{0}^{1,\alpha}(\Bar{B_R})$ of the singular equations $-\Delta_p u-\frac{1}{u^\delta}=f(x)$ and $-\Delta_p v-\frac{1}{v^\delta}=g(x)$ in $B_R$. Here we assume that $ 1 2$ a counterexample is provided where the strong comparison principle is violated. As an application of strong comparison principle, we prove a three solution theorem for p-Laplace equation and illustrate with an example.

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R. Dhanya, M. S. Indulekha, Ritabrata Jana. 2022-03-22. Strong comparison principle for a p-Laplace equation involving singularity and its applications. https://arxiv.org/abs/2203.11477

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