Discussion on integrable properties for higher-dimensional variable-coefficient nonlinear partial differential equations

2013 ◽  
Vol 54 (1) ◽  
pp. 013516 ◽  
Author(s):  
Yufeng Zhang ◽  
Honwah Tam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Variable Coefficient ◽  
Nonlinear Partial Differential Equations ◽  
Partial Differential ◽  
Higher Dimensional ◽  
Dimensional Variable

scholarly journals Integrable Equations and Their Evolutions Based on Intrinsic Geometry of Riemann Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Paul Bracken
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Partial Differential ◽  
Intrinsic Geometry ◽  
Integrable Equations ◽  
Higher Dimensional ◽  
Riemannian Spaces

The intrinsic geometry of surfaces and Riemannian spaces will be investigated. It is shown that many nonlinear partial differential equations with physical applications and soliton solutions can be determined from the components of the relevant metric for the space. The manifolds of interest are surfaces and higher-dimensional Riemannian spaces. Methods for specifying integrable evolutions of surfaces by means of these equations will also be presented.

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Partial Differential Equations ◽  
Dirichlet Boundary Conditions ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Lyapunov Inequalities ◽  
Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

Sign in / Sign up

Export Citation Format

Share Document