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Multiplicity of Solution for Some Classes of Prescribed Mean Curvature Equation with Dirichlet Boundary Condition

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Abstract

In this paper, we establish the existence of infinite many solutions for a class of prescribed mean curvature equation of the type

$$\begin{aligned} {\left\{ \begin{array}{ll} &{}-div\left( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}} \right) =f(u),\;\;\text{ in }\;\;\Omega ,\\ &{}u=0,\quad \text{ on }\quad \partial \Omega , \end{array}\right. } \end{aligned}$$

where \(\Omega \subset {\mathbb {R}}^N (N \ge 1)\) is a smooth bounded domain, by assuming different conditions on the nonlinearity f.

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Acknowledgements

The authors warmly thank the anonymous referee for her/his nice comments on the paper.

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Authors and Affiliations

  1. Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB, 58429-970, Brazil

    Claudianor O. Alves

  2. Instituto de investigación en matemáticas, Facultad de Ciencias Físicas y Matemáticas, Universidad Nacional de Trujillo, Av. Juan Pablo II s/n., Trujillo, Peru

    César E. Torres Ledesma

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Correspondence to César E. Torres Ledesma.

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C. O. Alves was partially supported by CNPq/Brazil 307045/2021-8, Projeto Universal FAPESQ 3031/2021. C. E. Torres Ledesma was partially supported by CONCYTEC, Peru, 379-2019-FONDECYT “ASPECTOS CUALITATIVOS DE ECUACIONES NO-LOCALES Y APLICACIONES.

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Alves, C.O., Ledesma, C.E.T. Multiplicity of Solution for Some Classes of Prescribed Mean Curvature Equation with Dirichlet Boundary Condition. J Geom Anal 32, 262 (2022). https://doi.org/10.1007/s12220-022-01010-1

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