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Liouville Results for Stable Solutions of Quasilinear Equations with Weights

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Abstract

This paper is devoted to the quasilinear equation

$$\left\{ \begin{gathered}- div\left( {w_1 \left| {\nabla u} \right|^{p - 2} \nabla u} \right) = w_2 f\left( u \right)in\Omega , \hfill \\u = 0on\partial \Omega , \hfill \\ \end{gathered} \right.$$

where p ≥ 2, Ω is a (bounded or unbounded) domain of ℝN, w1,w2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω, w1, w2 and f, which extends and unifies several results on this topic.

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Authors and Affiliations

  1. Department of Mathematical Economics, Banking University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

    Phuong Le

  2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vu Ho

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Vu Ho

Authors
  1. Phuong Le
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  2. Vu Ho
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Correspondence to Vu Ho.

Additional information

This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2017.307.

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Le, P., Ho, V. Liouville Results for Stable Solutions of Quasilinear Equations with Weights. Acta Math Sci 39, 357–368 (2019). https://doi.org/10.1007/s10473-019-0202-x

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  • DOI: https://doi.org/10.1007/s10473-019-0202-x

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