一类次线性基尔霍夫方程基态解的存在性

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  • School of Science, Tianjin University of Technology and Education, Tianjin 300222, China
XU Na (1986-), female, native of Baoding, Hebei, lecturer of Tianjin University of Technology and Education, engages in nonlinear analysis.

收稿日期: 2022-11-14

  网络出版日期: 2023-12-30

The Existence of Ground State Solutions for a Class of Sublinear Kirchhoff Equations

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  • School of Science, Tianjin University of Technology and Education, Tianjin 300222, China
XU Na (1986-), female, native of Baoding, Hebei, lecturer of Tianjin University of Technology and Education, engages in nonlinear analysis.

Received date: 2022-11-14

  Online published: 2023-12-30

摘要

In this paper,  we study  a class of sublinear Kirchhoff equations:
- (a+  b \int_{\mathbb{R}^N} |\nabla u|^2dx)\Delta u+ V(x)u =f(x,u) \  \   &\text{in}\ \mathbb{R}^N,
where a,b>0, V :RN→R can be sign-changing, and f :RN×R→R. Under some conditions on V and f, we verify that the problem possesses   at least one energy  solution by using variational method.

本文引用格式

许娜 . 一类次线性基尔霍夫方程基态解的存在性[J]. 数学季刊, 2023 , 38(4) : 410 -414 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.008

Abstract

In this paper,  we study  a class of sublinear Kirchhoff equations:
- (a+  b \int_{\mathbb{R}^N} |\nabla u|^2dx)\Delta u+ V(x)u =f(x,u) \  \   &\text{in}\ \mathbb{R}^N,
where a,b>0, V :RN→R can be sign-changing, and f :RN×R→R. Under some conditions on V and f, we verify that the problem possesses   at least one energy  solution by using variational method.
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