Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator

Rui Liu; Lin Li; Donal O’Regan

doi:10.1007/s12346-023-00879-9

Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator

Rui Liu, Lin Li, Donal O’Regan

Mathematics

Chongqing Technology and Business University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

In this work, we study the existence of a nontrivial bounded variation solution to a class of nonlocal elliptic problems of Kirchhoff type involving the 1-Laplacian operator in the whole space R^N and we will work with the space of functions of bounded variation. The Mountain Pass Theorem shows the existence of a nontrivial solution when f is an asymptotically constant nonlinearity.

Original language	English
Article number	24
Journal	Qualitative Theory of Dynamical Systems
Volume	23
Issue number	1
DOIs	https://doi.org/10.1007/s12346-023-00879-9
Publication status	Published - Feb 2024

Keywords

1-Laplacian operator
Kirchhoff type
Mountain pass theorem
Variational methods

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10.1007/s12346-023-00879-9

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abstract = "In this work, we study the existence of a nontrivial bounded variation solution to a class of nonlocal elliptic problems of Kirchhoff type involving the 1-Laplacian operator in the whole space RN and we will work with the space of functions of bounded variation. The Mountain Pass Theorem shows the existence of a nontrivial solution when f is an asymptotically constant nonlinearity.",

keywords = "1-Laplacian operator, Kirchhoff type, Mountain pass theorem, Variational methods",

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AB - In this work, we study the existence of a nontrivial bounded variation solution to a class of nonlocal elliptic problems of Kirchhoff type involving the 1-Laplacian operator in the whole space RN and we will work with the space of functions of bounded variation. The Mountain Pass Theorem shows the existence of a nontrivial solution when f is an asymptotically constant nonlinearity.

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KW - Kirchhoff type

KW - Mountain pass theorem

KW - Variational methods

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Bounded Variation Solution for a Class of Kirchhoff Type Problem Involving the 1-Laplacian Operator

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