Article Sidebar

Tiếng Việt
Date Published: 31/07/2025
Abstract Views: 300
Views Tiếng Việt: 92
DOI: 10.54607/hcmue.js.22.7.4023(2025)
Issue
Tập 22, số 7(2025)
Section
Articles
How to Cite
Nguyen, N. H. T. (2025). EIGENVALUE ROBIN PROBLEM FOR THE P-LAPLACIAN WITH WEIGHT. Ho Chi Minh City University of Education Journal of Science, 22(7), 1189-1198. https://doi.org/10.54607/hcmue.js.22.7.4023(2025)

EIGENVALUE ROBIN PROBLEM FOR THE P-LAPLACIAN WITH WEIGHT

Nguyen Ngoc Huy Truong1,
1 Ho Chi Minh City University of Education

Main Article Content

Abstract

The eigenvalue problem is an essential part of mathematics and is often encountered in various fields, such as computer science, engineering, physics, and many others. Properties of eigenvalues have attracted the attention of mathematicians for centuries. In this paper, we conducted a study on the existence of a non-negative, non-decreasing sequence of eigenvalues for p-Laplacian and the closedness property of the set of these eigenvalues. Specifically, the study explores the boundedness and Hölder continuity of eigenfunctions under Robin boundary conditions. This investigation involves a function  defined on the boundary , which is not necessarily continuous but satisfies and .

Keywords

Eigenvalue problem, p-Laplacian, Robin boundary conditions with weights

Article Details

References

Allegretto, W., & Huang, Y. X. (1998). A Picone’s identity for the p-Laplacian and applications. Nonlinear Analysis, 32(7), 819-830. https://doi.org/10.1016/s0362-546x(97)00530-0
Anane, A. (1987). Étude des valeurs propres et de la résonance pour l'opérateur p-Laplacien [Study of eigenvalues and resonance for the p-Laplacian operator]. Comptes Rendus de l'Académie des Sciences de Paris, 305, 725-728.
Arouzi, G. A., & Khademloo, S. (2007). Principal eigenvalues of the p-Laplacian with the boundary condition involving indefinite weight. World Journal of Modelling and Simulation, 3(4), 299-304.
Browder, F. (1970). Existence theorems for nonlinear partial differential equations. In Global analysis, Proceedings of the Symposium Pure Mathematics (Vol. XVI, Berkeley, California, 1968, pp. 1-60). American Mathematical Society. https://doi.org/10.1090/pspum/016/0269962
Cuesta, M. (2001). Eigenvalue problems for the p-Laplacian with indefinite weights. Electronic Journal of Differential Equations, 2001(33), 1-9.
Deng, S. G. (2009). Positive solutions for Robin problem involving the p(x)-Laplacian. Journal of Mathematical Analysis and Applications, 360(2), 548-560. https://doi.org/10.1016/j.jmaa.2009.06.032
Huang, Y. X. (1990). On eigenvalue problems of the p-Laplacian with Neumann boundary conditions. Proceedings of the American Mathematical Society, 109, 177-184. https://doi.org/10.2307/2048377
Le, A. (2006). Eigenvalue problems for the p-Laplacian. Nonlinear Analysis: Theory, Methods & Applications, 64(5), 1057-1099. https://doi.org/10.1016/j.na.2005.05.056
Le, V. K., & Schmitt, K. (1997). Global Bifurcation in Variational Inequalities: Applications to Obstacle and Unilateral Problems. Springer. https://doi.org/10.1007/978-1-4612-1820-3
Rahmani, M., Tsouli, N., Darhouche, O., & Chakrone, O. (2012). Eigenvalue Robin problem for the p-Laplacian with weight. Journal of Abstract Differential Equations and Applications, 3(2), 60-74.
Torne, O. (2005). Steklov problem with an indefinite weight for the p-Laplacian. Electronic Journal of Differential Equations, 2005(87), 1-8.
Zeidler, E. (1980). The Ljusternik-Schnirelman theory for indefinite and not necessarily odd nonlinear operators and its applications. Nonlinear Analysis: Theory, Methods & Applications, 4(3), 451-489. https://doi.org/10.1016/0362-546x(80)90085-1