scholarly journals On a Generalized Sturm Theorem

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Alessandro Portaluri
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Oscillation Theorem ◽  
Second Order Differential Equations ◽  
Indefinite Systems ◽  
Sturm Theorem ◽  
Type Oscillation

AbstractSturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm type oscillation theorem for indefinite systems with Dirichlet boundary conditions of the formwhere p

scholarly journals ESTIMATION OF TURNING POINT LOCATION OF CONVEX SOLUTIONS FOR NONLINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 17 (5) ◽  
pp. 642-649
Author(s):  
Robert Vrabel
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Turning Point ◽  
Dirichlet Boundary ◽  
Upper Bounds ◽  
Dirichlet Boundary Conditions ◽  
Lower And Upper Bounds ◽  
Point Location ◽  
Second Order Differential Equations

In this paper, we study the existence and location of turning points of the convex solutions for a certain class of the ordinary differential equations subject to the Dirichlet boundary conditions. We propose a practical and effective method for calculating the lower and upper bounds of turning point location.

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.

scholarly journals A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem

2021 ◽  
Vol 14 (3) ◽  
pp. 706-722
Author(s):  
Francis Ohene Boateng ◽  
Joseph Ackora-Prah ◽  
Benedict Barnes ◽  
John Amoah-Mensah
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Finite Difference Methods ◽  
Dirichlet Boundary Conditions ◽  
Fictitious Domain ◽  
Dirichlet Boundary Value Problem ◽  
Wavelet Method ◽  
Difference Methods

In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic  partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods.

scholarly journals The nonlocal mean-field equation on an interval

2019 ◽  
Vol 22 (05) ◽  
pp. 1950028
Author(s):  
Azahara DelaTorre ◽  
Ali Hyder ◽  
Luca Martinazzi ◽  
Yannick Sire
Keyword(s):  
Field Equation ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mean Field ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Field Equations ◽  
Mean Field Equations ◽  
Blowing Up ◽  
Mean Field Equation

We consider the fractional mean-field equation on the interval [Formula: see text] [Formula: see text] subject to Dirichlet boundary conditions, and prove that existence holds if and only if [Formula: see text]. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.

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