scholarly journals On the Existence of Non-Spurious Solutions to Second Order Dirichlet Problem

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 231
Author(s):  
Michał Bełdziński ◽  
Tomasz Gałaj ◽  
Radosław Bednarski ◽  
Filip Pietrusiak ◽  
Marek Galewski ◽  
...  
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Convex Function ◽  
Second Order ◽  
New Approach ◽  
Spurious Solutions ◽  
Direct Variational Method ◽  
Discrete Family

Using the direct variational method together with the monotonicity approach we consider the existence of non-spurious solutions to the following Dirichlet problem −x¨t =ft,xt, x0 =x1 =0, where f: 0,1 × R→R is a jointly continuous and not necessarily convex function. A new approach towards deriving the discrete family of approximating problems is proposed.

Multiple solutions for semi-linear corner degenerate elliptic equations with singular potential term

2016 ◽  
Vol 19 (04) ◽  
pp. 1650043 ◽  
Author(s):  
Hua Chen ◽  
Shuying Tian ◽  
Yawei Wei
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Singular Potential ◽  
Degenerate Elliptic Equations ◽  
Dirichlet Boundary Value Problem ◽  
Potential Term ◽  
Degenerate Elliptic

The present paper is concern with the Dirichlet problem for semi-linear corner degenerate elliptic equations with singular potential term. We first give the preliminary of the framework and then discuss the weighted corner type Hardy inequality. By using the variational method, we prove the existence of multiple solutions for the Dirichlet boundary-value problem.

One method for the boundary value problem eigenvalues calcuating for a second-order differential equation with a fractional derivative

2019 ◽  
Vol 10 (01) ◽  
pp. 1941004
Author(s):  
Temirkhan Aleroev ◽  
Hedi Aleroeva ◽  
Lyudmila Kirianova
Keyword(s):  
Differential Equation ◽  
Perturbation Theory ◽  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Second Order ◽  
Linear Operators

In this paper, we give a formula for computing the eigenvalues of the Dirichlet problem for a differential equation of second-order with fractional derivatives in the lower terms. We obtained this formula using the perturbation theory for linear operators. Using this formula we can write out the system of eigenvalues for the problem under consideration.

Ferroelectricity enhancement in confined nanorods: Direct variational method

2006 ◽  
Vol 73 (21) ◽  
Author(s):  
Anna N. Morozovska ◽  
Eugene A. Eliseev ◽  
Maya D. Glinchuk
Keyword(s):  
Variational Method ◽  
Direct Variational Method
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