Existence of solutions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si4.svg"><mml:mi>p</mml:mi></mml:math>-Laplacian parabolic Kirchhoff equation

Chen, Wenjing; Zhou, Ting

doi:10.1016/j.aml.2021.107527

Cited by 5 publications

(7 citation statements)

References 13 publications

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“…Variational inequalities are often used to quantify consumption-investment models [12,13] which contain two factors…”

Section: The Main Results and The Financial Backgroundmentioning

confidence: 99%

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Existence, Blow-Up, and Blow-Up Rate of Weak Solution to Fourth-Order Non-Newtonian Polytropic Variation-Inequality Arising from Consumption-Investment Models

Li,

Bai

2024

Journal of Mathematics

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This article obtains the conditions for the existence and nonexistence of weak solutions for a variation-inequality problem. This variational inequality is constructed by a fourth-order non-Newtonian polytropic operator which is receiving much attention recently. Under the proper condition of the parameter, the existence of a solution is proved by constructing the initial boundary value problem of an ellipse by time discretization and some elliptic equation theory. Under the opposite parameter condition, we analyze the nonexistence of the solution. The results show that the weak solution will blow up in finite time. Finally, we give the blow-up rate and the upper bound of the blow-up time.

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“…Variational inequalities are often used to quantify consumption-investment models [12,13] which contain two factors…”

Section: The Main Results and The Financial Backgroundmentioning

confidence: 99%

“…Denote the classical solution of problem ( 9) by u ε , whose existence follows, for example, from Teorem 1.1 of [12], such that one can have the weak equation…”

Section: The Main Results and The Financial Backgroundmentioning

confidence: 99%

Existence, Blow-Up, and Blow-Up Rate of Weak Solution to Fourth-Order Non-Newtonian Polytropic Variation-Inequality Arising from Consumption-Investment Models

Li,

Bai

2024

Journal of Mathematics

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“…Thus, we find (e). Using Aubin-Lions lemma [4] , M (•, θ) is a compact operator, then (c) holds. We omit the details here.…”

Section: The Application Of Leray-schauder Principlementioning

confidence: 96%

“…With critical exponential growth condition , Huang and Deng [2] proved the existence of solution for Kirchhoff type problem . Later, some papers [3,4] also studied the Kirchhoff type problems with local nonlinear terms. The existence of solutions was studied, after adding some conditions appropriately.…”

Section: Introductionmentioning

confidence: 99%

“…The first innovation of this paper is to study a kind of variation-inequality problem under Kirchhoff operator based on variable exponent p(x). Reference [1][2][3][4][5][6][7][8][9][10][11][12][13] studied the initial boundary value problem with Kirchhoff operator. In this paper, we study a class of variational inequality problems with Kirchhoff operator.…”

Section: Introductionmentioning

confidence: 99%

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Study of weak solutions for a p(x)-Kirchhoff type variation-inequality problems arising from financial problems

Li¹,

Bai²

2023

Preprint

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In this paper, we study variation-inequality initial-boundary value problems with variable parameter Kirchhoff operators. We constructed a map suitable for the Leray-Schauder principle in which the existence of solution is proved. The uniqueness and stability of the solution are also analyzed under a smallness condition on the parameter of Kirchhoff operators. Mathematics Subject Classification 2010: 35K99, 97M30.

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Weak solution of non-Newtonian polytropic variational inequality in fresh agricultural product supply chain problem

2023

Open Mathematics

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In this article, we study a class of variational inequality problems with non-Newtonian polytropic parabolic operators. We introduce a mapping with an adjustable parameter to control the polytropic term, which exactly meets the conditions of Leray-Schauder fixed point theory. At the same time, we construct a penalty function to transform the variational inequality into a regular parabolic initial boundary value problem. Thus, the existence is treated with a Leray-Schauder fixed point theory as well as a suitable version of Aubin-Lions lemma. Then, the uniqueness and stability of the solution are analyzed.

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Existence of solutions for p-Laplacian parabolic Kirchhoff equation

Cited by 5 publications

References 13 publications

Existence, Blow-Up, and Blow-Up Rate of Weak Solution to Fourth-Order Non-Newtonian Polytropic Variation-Inequality Arising from Consumption-Investment Models

Existence, Blow-Up, and Blow-Up Rate of Weak Solution to Fourth-Order Non-Newtonian Polytropic Variation-Inequality Arising from Consumption-Investment Models

Study of weak solutions for a p(x)-Kirchhoff type variation-inequality problems arising from financial problems

Weak solution of non-Newtonian polytropic variational inequality in fresh agricultural product supply chain problem

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