Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R3
Gongbao Li,Hongyu Ye +1 more
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In this article, the authors studied the nonlinear problem of Kirchhoff type with pure power nonlinearities and proved that (0.1) has a positive ground state solution by using a monotonicity trick and a new version of global compactness lemma.About:
This article is published in Journal of Differential Equations.The article was published on 2014-07-15 and is currently open access. It has received 310 citations till now. The article focuses on the topics: Kirchhoff equations.read more
Citations
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Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in R3
TL;DR: In this paper, the authors studied the existence and asymptotic behavior of nodal solutions to the following Kirchhoff problem − (a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( | x | ) u = f( | x|, u ), in R 3, u ∈ H 1 ( R 3 ), where V ( x ) is a smooth function, a, b are positive constants.
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Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities
TL;DR: In this article, the existence and concentration behaviors of positive solutions to the Kirchhoff type equations were studied under suitable conditions on M and general conditions on f, where M and V are continuous functions.
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Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains☆
TL;DR: In this article, the existence of least energy sign-changing solutions for a class of Kirchhoff-type problems in bounded domains has been studied in the context of constraint variational method and quantitative deformation lemma.
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Ground state sign-changing solutions for Kirchhoff type problems in bounded domains ☆
Xianhua Tang,Bitao Cheng +1 more
TL;DR: In this paper, the authors considered the existence of ground state sign-changing solutions for a class of Kirchhoff-type problems (0.1) and proved that the energy of the ground state solution is strictly larger than twice that of the non-Neighari-type ground state solutions.
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Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials
Xianhua Tang,Sitong Chen +1 more
TL;DR: Li et al. as mentioned in this paper studied the following Kirchhoff-type problem 0.1 and showed that it admits a ground state solution of the Nehari-Pohozaev type and a least energy solution under some mild assumptions on V and f.
References
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Nonlinear scalar field equations, I existence of a ground state
TL;DR: In this article, a constrained minimization method was proposed for the case of dimension N = 1 (Necessary and sufficient conditions) for the zero mass case, where N is the number of dimensions in the dimension N.
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The concentration-compactness principle in the calculus of variations. The locally compact case, part 1
TL;DR: In this paper, the equivalence between the compactness of all minimizing sequences and some strict sub-additivity conditions was shown based on a compactness lemma obtained with the help of the notion of concentration function of a measure.
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Regularity for a more general class of quasilinear elliptic equations
TL;DR: On considere des solutions u∈H 1,p (Ω)∧L ∞ ( Ω) (1
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C1 + α local regularity of weak solutions of degenerate elliptic equations
TL;DR: In this article, the local C(1 + Alpha) nature of weak solutions of elliptic equations of the type (1.1) in the introduction under the degeneracy (or singularity) assumptions (A sub 1)-(A sub 3).
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