Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3

By Gongbao Li, Hongyu Ye. 2014

389 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ba5a7ad753379c4459b57688933497adf4b8a4fa

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In Applied Mathematics

1. Xianhua Tang
2. Gongbao Li
3. Sitong Chen
4. Xiaoyutao Luo
5. Hongyu Ye
6. Tao Yang
7. Huan-Song Zhou
8. Yimin Zhang

In Control and Systems Engineering

1. Xiaoyutao Luo
2. Xianhua Tang
3. Gongbao Li
4. Sitong Chen
5. Yimin Zhang
6. Huan-Song Zhou
7. Helin Guo
8. Hongyu Ye

In Mathematical Physics

1. Xiaoyutao Luo
2. Xianhua Tang
3. Sitong Chen
4. Gongbao Li
5. Tao Yang
6. Hongyu Ye
7. Chang-Lin Xiang
8. Shuangjie Peng

Citations in the corpus

• Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, neutral): “3), we refer to [5,17,18,24,27–30,36].”
• Blow-up solutions for a Kirchhoff type elliptic equation with trapping potential (2017, methodology): “1) with λ = 0 and p ∈ (1, 4) was discussed in [18] and a positive ground state solution was found by solving a constrained minimization over a Nehari-Pohozaev type manifold.”
• The sharp existence of constrained minimizers for a class of nonlinear Kirchhoff equations (2015, methodology): “Moreover, u satisfies the following Pohozaev identity [17]:”
• Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials (2017, methodology): “Different from [23], Guo [16] defined a new manifold M̄ = {u ∈ H1(R3) : 1 2 〈 ′(u), u〉 + P(u) = 0} (it will be called the Nehari–Pohozaev manifold), where (u) = 1 2 ∫ R3 (a|∇u|2 + u2)dx + b 4 (∫”
• Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, background): “2), we mention work by [8,9,47].”
• A singularly perturbed Kirchhoff problem revisited (2016, methodology): “In particular, in the papers of Ye [35] and Li and Ye [26], to apply the Mountain Pass Lemma to find a ground state solution, quite complicated manifolds were constructed in order to find a bounded Palais-Smale sequence.”
• Normalized solutions to a class of Kirchhoff equations with Sobolev critical exponent (2021, background): “One can refer to [1, 6, 8, 12, 13, 20, 9] and the references therein for more mathematical and physical background of (1.”