跳至主要内容

Generalized Spectrum of Steklov-Robin Type Problem for Elliptic Systems

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=54176#.VPAodyzQrzE

We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive measure. We prove the existence of an increasing unbounded sequence of eigenvalues. The method of proof makes use of variational arguments.
Cite this paper
Fadlallah, A. , Antwi-Fordjour, K. and Nkashama, M. (2015) Generalized Spectrum of Steklov-Robin Type Problem for Elliptic Systems. Applied Mathematics, 6, 421-429. doi: 10.4236/am.2015.62039.
 

[1] Auchmuty, G. (2012) Bases and Comparison Results for Linear Elliptic Eigenproblems. Journal of Mathematical Analysis and Applications, 390, 394-406.
http://dx.doi.org/10.1016/j.jmaa.2012.01.051
[2] Mavinga, N. (2012) Generalized Eigenproblem and Nonlinear Elliptic Equations with Nonlinear Boundary Conditions. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 142, 137-153.
[3] de Godoi, J.D.B., Miyagaki, O.H. and Rodrigues, R.S. (2013) Steklov-Neumann Eigenvalue Problems for a Class of Elliptic System. SP-Brazil.
[4] Steklov, L.M.W. (1902) Sur les problèmes fundamentaux de la physique mathématique. Annali Scuola Norm. Sup. Pisa, 19, 455-490.
[5] Küfner, A., John, O. and Fucik, S. (1977) Function Spaces. Noordhoff International Publishing, Leyden.
[6] Necas, J. (1967) Les Mèthodes directes en thèorie des equations elliptiques. Masson, Paris.
[7] Grisvard, P. (1985) Elliptic Problems in Nonsmooth Domains. Pitman, Boston.
[8] Fadlallah, A. (2015) Elliptic Equations and Systems with Nonlinear Boundary Conditions. Ph.D. Dissertation, University of Alabama at Birmingham (UAB), Birmingham.                    eww150225lx

评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...