scholarly journals Variational Method to p-Laplacian Fractional Dirichlet Problem with Instantaneous and Noninstantaneous Impulses

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Yiru Chen ◽  
Haibo Gu ◽  
Lina Ma
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Existence Results ◽  
Major Result ◽  
Dirichlet Boundary Value Problem ◽  
Fractional Differential ◽  
Noninstantaneous Impulses

In this paper, a research has been done about the existence of solutions to the Dirichlet boundary value problem for p-Laplacian fractional differential equations which include instantaneous and noninstantaneous impulses. Based on the critical point principle and variational method, we provide the equivalence between the classical and weak solutions of the problem, and the existence results of classical solution for our equations are established. Finally, an example is given to illustrate the major result.

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.

scholarly journals Existence Results for a System of Coupled Hybrid Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas ◽  
Ahmed Alsaedi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Uniqueness Result ◽  
Existence Results ◽  
Dirichlet Boundary Conditions ◽  
Fractional Differential

This paper studies the existence of solutions for a system of coupled hybrid fractional differential equations with Dirichlet boundary conditions. We make use of the standard tools of the fixed point theory to establish the main results. The existence and uniqueness result is elaborated with the aid of an example.

scholarly journals Existence results for a sublinear second order Dirichlet boundary value problem on the half-line

2020 ◽  
Vol 40 (5) ◽  
pp. 537-548
Author(s):  
Dahmane Bouafia ◽  
Toufik Moussaoui
Keyword(s):  
Variational Principle ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Point Theory ◽  
Existence Results ◽  
Half Line ◽  
Dirichlet Boundary Value Problem ◽  
Nontrivial Solutions

In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland's variational principle and critical point theory.

scholarly journals About the Dirichlet Boundary Value Problem using Clifford Algebras

2018 ◽  
Vol 15 ◽  
pp. 8098-8119
Author(s):  
Johan Ceballos
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Clifford Algebras ◽  
Dirichlet Boundary ◽  
Relevant Literature ◽  
Monogenic Functions ◽  
Dirichlet Boundary Value Problem ◽  
Dirichlet Problems ◽  
Initial Value ◽  
Do So

This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to solve an initial value problem related to a fibre.

scholarly journals Some Existence Results of Positive Solutions forφ-Laplacian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xianghui Xu ◽  
Yong-Hoon Lee
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Existence Results ◽  
Dirichlet Boundary Value Problem ◽  
Singular Weight ◽  
Existence Of Positive Solutions

We study the existence of positive solutions for the homogeneous Dirichlet boundary value problem ofφ-Laplacian systems with a singular weight which may not be inL1.

scholarly journals Existence of solutions to an impulsive Dirichlet boundary value problem

2018 ◽  
Vol 19 (1) ◽  
pp. 225-234 ◽  
Author(s):  
John R. Graef ◽  
◽  
Shapour Heidarkhani ◽  
Lingju Kong ◽  
◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem

scholarly journals Dirichlet Problem for Maximal Graphs of Higher Codimension

2020 ◽  
Author(s):  
Yang Li
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Dirichlet Boundary Value Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
General Existence

Abstract We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian-type ambient spaces and obtain general existence and uniqueness results that apply to any codimension.

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