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Least energy sign-changing solutions for a class of nonlocal Kirchhoff-type problems

机译：一类非局部Kirchhoff型问题的最小能量符号转换解决方案

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摘要

In this paper, we consider the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem

\begin{matrix} \{\begin{matrix} - (a + b \int_{Ω} {| \nabla u |}^{2} d x) Δ u = g (x, u), & x \in Ω, \\ u = 0, & x \in \partial Ω, \end{matrix} (K_{b}) \end{matrix}

where Ω is a bounded domain in ℝ^N, N = 1, 2, 3, with a smooth boundary ∂Ω, a 0, b 0 and g ∈ C⁰(Ω × ℝ, ℝ). By using variational approach and some subtle analytical skills, the existence of the least energy sign-changing solutions of (Kb) is obtained successfully. Moreover, we prove that the energy of any sign-changing solutions is larger than twice that of the ground state solutions of (Kb).

机译：在本文中，我们考虑了一类Kirchhoff型问题的最小能量符号转换解决方案的存在。

<行> <行> \begin{matrix} -“（”a+b\intΩ< / mi>|\nablau|2dxΔu=g（< mi> x，u），“）” \end{matrix}

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期刊名称 SpringerPlus
作者
Bitao Cheng;
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作者单位

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年(卷),期 -1(5),1
年度 -1
页码 1256
总页数 9
原文格式 PDF
正文语种
中图分类
关键词
Kirchhoff-type problem Least energy sign-changing solutions Variational approach;

机译：基尔霍夫型问题;最小能量符号转换解决方案;变分方法;

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1. Ground state solutions and least energy sign-changing solutions for a class of fourth order Kirchhoff-type equations in R N [J] . Sofiane Khoutir, Haibo Chen Arab Journal of Mathematical Sciences . 2017,第1期

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2. Least energy sign-changing solutions for a class of fourth order Kirchhoff-type equations in RN [J] . Sofiane Khoutir, Haibo Chen Journal of Applied Mathematics and Computing . 2017,第1a2期

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3. Existence of sign-changing solution with least energy for a class of Kirchhoff-type equations in RN [J] . Xianzhong Yao, Chunlai Mu Electronic Journal of Qualitative Theory of Differential Equations . 2017,第32期

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4. A Note on Non-radial Sign-changing Solutions for the Schr?dinger-Poisson Problem in the Semiclassical Limit [C] . Giusi Vaira School and Workshop on Cocompact Imbeddings, Profile Decompositions, and their Applicatons to PDE . 2013

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5. Axisymmetric problems in nonlinear elasticity: Existence and global injectivity of energy minimizers and new classes of exact solutions. [D] . Novozhilova, Lydia S. 2004

机译：非线性弹性中的轴对称问题：能量最小化器的存在和整体注入以及新型的精确解。
6. Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian [O] . Liejun Shen -1

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7. Least energy sign-changing solutions for a class of nonlocal Kirchhoff-type problems [O] . Bitao Cheng 2016

机译：一类非局部Kirchhoff型问题的最小能量符号转换解决方案

Least energy sign-changing solutions for a class of nonlocal Kirchhoff-type problems

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