scholarly journals Radial solutions of a fourth order Hamiltonian stationary equation

2018 ◽  
Vol 265 (4) ◽  
pp. 1576-1595 ◽  
Author(s):  
Jingyi Chen ◽  
Micah Warren
Keyword(s):  
Fourth Order ◽  
Radial Solutions ◽  
Stationary Equation ◽  
Hamiltonian Stationary

scholarly journals Weighted fourth order elliptic problems in the unit ball

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zongming Guo ◽  
Fangshu Wan
Keyword(s):  
Asymptotic Behavior ◽  
Singular Point ◽  
Unit Ball ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Spaces ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Uniqueness Results ◽  
Positive Radial Solutions

<p style='text-indent:20px;'>Existence and uniqueness of positive radial solutions of some weighted fourth order elliptic Navier and Dirichlet problems in the unit ball <inline-formula><tex-math id="M1">\begin{document}$ B $\end{document}</tex-math></inline-formula> are studied. The weights can be singular at <inline-formula><tex-math id="M2">\begin{document}$ x = 0 \in B $\end{document}</tex-math></inline-formula>. Existence of positive radial solutions of the problems is obtained via variational methods in the weighted Sobolev spaces. To obtain the uniqueness results, we need to know exactly the asymptotic behavior of the solutions at the singular point <inline-formula><tex-math id="M3">\begin{document}$ x = 0 $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Analysis and Computation of Solutions for a Class of Nonlinear SBVPs Arising in Epitaxial Growth

2021 ◽  
Author(s):  
Amit K Verma ◽  
Biswajit Panditt ◽  
Ravi P Agarwal
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Molecular Beam Epitaxy ◽  
Fourth Order ◽  
Molecular Beam ◽  
Order Differential Equation ◽  
Elliptic Partial Differential Equation ◽  
Radial Solutions ◽  
Existence And Nonexistence ◽  
Fourth Order Differential Equation

In this work the existence and nonexistence of stationary radial solutions to the elliptic partial differential equation arising in the molecular beam epitaxy are studied. Since we are interested in radial solutions we arrive at the following fourth-order differential equation

Radial solutions of inhomogeneous fourth order elliptic equations and weighted Sobolev embeddings

2015 ◽  
Vol 4 (2) ◽  
pp. 135-151 ◽  
Author(s):  
Reginaldo Demarque ◽  
Olimpio H. Miyagaki
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Elliptic Problems ◽  
Continuous Functions ◽  
Existence Results ◽  
Compact Embedding ◽  
Biharmonic Operator ◽  
Radial Solutions ◽  
Sobolev Embeddings ◽  
Fourth Order Elliptic Equations

AbstractWe deal with a class of inhomogeneous elliptic problems involving the biharmonic operator Δ2u + V(|x|)|u|q-2u = Q(|x|)f(u), u ∈ D02,2(ℝN), where Δ2 is the biharmonic operator and V, Q are singular continuous functions. Compact embedding results are established and by using these facts some existence results are obtained.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

Exploring the Fourth Order

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Barend KLITSIE ◽  
Rebecca PRICE ◽  
Christine DE LILLE
Keyword(s):  
Action Research ◽  
Fourth Order ◽  
Subject Matter ◽  
Action Research Project ◽  
Research Project ◽  
Building Trust ◽  
Current Business

Companies are organised to fulfil two distinctive functions: efficient and resilient exploitation of current business and parallel exploration of new possibilities. For the latter, companies require strong organisational infrastructure such as team compositions and functional structures to ensure exploration remains effective. This paper explores the potential for designing organisational infrastructure to be part of fourth order subject matter. In particular, it explores how organisational infrastructure could be designed in the context of an exploratory unit, operating in a large heritage airline. This paper leverages insights from a long-term action research project and finds that building trust and shared frames are crucial to designing infrastructure that affords the greater explorative agenda of an organisation.

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