Multiple Solutions for a Non-cooperative Elliptic System of Kirchhoff Type Involving p$p$-Biharmonic Operator and Critical Growth

Chung, Nguyen Thanh

doi:10.1007/s10440-019-00237-5

Cited by 3 publications

(3 citation statements)

References 28 publications

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“…In 2020, similar results were also obtained by N. T. Chung [15] for the Kirchhoff-type system with a p-biharmonic operator.…”

Section: Lsupporting

confidence: 72%

“…The novelty of this paper is as follows: in all the aforementioned papers, limit index theory [16] was applied, but the (PS) * c condition, which is described in Definition 2, should be considered. However, in the papers of Chung [15,20], Chems Eddine [21], Liang and Shi [17], Liang and Zhang [14,18,19], Li and Song [22], Sun and Bai et al [23], and Song and Shi [24], with the concentration-compactness principle [25], the boundness of the (PS)…”

Section: Lmentioning

confidence: 99%

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Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

Mao,

Yang

2024

Axioms

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Considering the solutions of a class of noncooperative Kirchhoff-type p(x)-Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain underlying assumptions. The novelty of this study is that we verify the (PS)c* condition using another method, diverging from the approaches cited in the previous literature.

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“…In 2020, similar results were also obtained by N. T. Chung [15] for the Kirchhoff-type system with a p-biharmonic operator.…”

Section: Lsupporting

confidence: 72%

Section: Lmentioning

confidence: 99%

Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

Mao,

Yang

2024

Axioms

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“…is a constant, then problem (3) has recently been the subject of extensive research. For example, in [12], Nguyen Thanh Chung studied the existence of non-trivial solutions for the following Kirchhoff-type system involving p-biharmonic operator…”

Section: Introductionmentioning

confidence: 99%

A Class of Fourth-Order Symmetrical Kirchhoff Type Systems

Taarabti

Allali

et al. 2022

Symmetry

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This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(·)&q(·)-Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri’s critical point theorem, we can find a proper conditions to ensure that the perturbed fourth-order of (p(x),q(x))-Kirchhoff systems has at least three weak solutions. We have extended and improved some recent results. The complexity of the combination of variable exponent theory and fourth-order Kirchhoff systems makes the results of this work novel and new contribution. Finally, a very concrete example is given to illustrate the applications of our results.

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Multiplicity of solutions for the noncooperative Choquard-Kirchhoff system involving Hardy-Littlewood-Sobolev critical exponent on the Heisenberg group

Sun

Yang

Song

2022

Rend. Circ. Mat. Palermo, II. Ser

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Multiple Solutions for a Non-cooperative Elliptic System of Kirchhoff Type Involving p$p$-Biharmonic Operator and Critical Growth

Cited by 3 publications

References 28 publications

Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

Multiplicity of Solutions for the Noncooperative Kirchhoff-Type Variable Exponent Elliptic System with Nonlinear Boundary Conditions

A Class of Fourth-Order Symmetrical Kirchhoff Type Systems

Multiplicity of solutions for the noncooperative Choquard-Kirchhoff system involving Hardy-Littlewood-Sobolev critical exponent on the Heisenberg group

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