Uniqueness in some higher order elliptic boundary value problems in n dimensional domains

Danet, Cristian-Paul

doi:10.14232/ejqtde.2011.1.54

Cited by 7 publications

(3 citation statements)

References 7 publications

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“…The case of n = 2, ϕ ≡ 0 and f (t) = k 1 t 3 + k 2 t with k 1 , k 2 > 0 arises in bending of cylindrical shells [16]. A uniqueness result for the corresponding boundary value problem under Dirichlet boundary conditions was given by Danet [3]. Equation (1.1) where n = 2, ϕ ≡ 0, ρ ≡ constant < 0 and f (t) = t arises in thin plate theory [15].…”

Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Weak and Classical Solutions for a Fourth-Order Semilinear Boundary Value Problem

Danet¹

2019

ANZIAM J.

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Section: Introductionmentioning

confidence: 99%

Existence and Uniqueness of Weak and Classical Solutions for a Fourth-Order Semilinear Boundary Value Problem

Danet¹

2019

ANZIAM J.

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“…was considered in many works, e.g., [3], [5], [11], [15], [19], [20], [27], [28], [35]. However, for boundary value problems of sixth order elliptic equations some results of uniqueness of solution are known in a few works such as [12], [14], [32]. In spite of these facts, there are many works concerning the numerical solution of nonlinear triharmonic boundary value problems, see e.g., [13], [21]- [24].…”

Section: Introductionmentioning

confidence: 99%

Existence Results and Numerical Method for a Fourth Order Nonlinear Problem

A¹,

Hương

2018

Int. J. Appl. Comput. Math

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In this work, we consider a boundary value problem for nonlinear triharmonic equation. Due to the reduction of nonlinear boundary value problems to operator equation for nonlinear terms we establish the existence, uniqueness and positivity of solution. More importantly, we design an iterative method at both continuous and discrete level for numerical solution of the problem. An analysis of actual total error of the obtained discrete solution is made. Some examples demonstrate the applicability of the theoretical results on qualitative aspects and the efficiency of the iterative method.

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“…For further uniqueness results (in higher dimensions) the reader is referred to the paper [7] and [8].…”

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confidence: 99%

The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach

Danet

2020

ITM Web Conf.

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This paper is concerned with the problem of existence and uniqueness of solutions for the semilinear fourth-order diﬀerential equation uiv – ku′′ + a(x)u+c(x) f (u) = 0. Existence and uniqueness is proved using variational methods and maximum principles. We also give a dynamical system approach to the equation. We study the bifurcation of the system and show that the behaviour of the stationary points S (α, 0, 0, 0) depend on the relation between the parameter k and β = f ′(α).

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Uniqueness in some higher order elliptic boundary value problems in n dimensional domains

Cited by 7 publications

References 7 publications

Existence and Uniqueness of Weak and Classical Solutions for a Fourth-Order Semilinear Boundary Value Problem

Existence and Uniqueness of Weak and Classical Solutions for a Fourth-Order Semilinear Boundary Value Problem

Existence Results and Numerical Method for a Fourth Order Nonlinear Problem

The study of a fourth-order differential equation: existence, uniqueness and a dynamical system approach

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