scholarly journals Boundary value problems of a discrete generalized beam equation via variational methods

2018 ◽  
Vol 16 (1) ◽  
pp. 1412-1422
Author(s):  
Xia Liu ◽  
Tao Zhou ◽  
Haiping Shi
Keyword(s):  
Variational Methods ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Beam Equation

AbstractThe authors explore the boundary value problems of a discrete generalized beam equation. Using the critical point theory, some sufficient conditions for the existence of the solutions are obtained. Several consequences of the main results are also presented. Examples are given to illustrate the theorems.

scholarly journals Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1207
Author(s):  
Feng Xiong ◽  
Zhan Zhou
Keyword(s):  
Dirichlet Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Laplacian Operator

In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example.

scholarly journals Existence of Weak Solutions for a New Class of Fractional p-Laplacian Boundary Value Systems

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 475 ◽  
Author(s):  
Fares Kamache ◽  
Rafik Guefaifia ◽  
Salah Boulaaras ◽  
Asma Alharbi
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Weak Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Existence Of Weak Solutions ◽  
New Class ◽  
Two Parameters

In this paper, at least three weak solutions were obtained for a new class of dual non-linear dual-Laplace systems according to two parameters by using variational methods combined with a critical point theory due to Bonano and Marano. Two examples are given to illustrate our main results applications.

scholarly journals A Variational Approach to Perturbed Discrete Anisotropic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Amjad Salari ◽  
Giuseppe Caristi ◽  
David Barilla ◽  
Alfio Puglisi
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Multiplicity Results ◽  
Anisotropic Equation

We continue the study of discrete anisotropic equations and we will provide new multiplicity results of the solutions for a discrete anisotropic equation. We investigate the existence of infinitely many solutions for a perturbed discrete anisotropic boundary value problem. The approach is based on variational methods and critical point theory.

Existence of the Solutions for a Class of Nonlinear Difference Systems Boundary Value Problem

2013 ◽  
Vol 281 ◽  
pp. 312-318
Author(s):  
Fang Su ◽  
Xue Wen Qin
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Difference Systems

In this paper, by using critical point theory, we obtain a new result on the existence of the solutions for a class of difference systems boundary value problems. Results obtained extend or improve existing ones.

TWO POSITIVE SOLUTIONS OF SOME SINGULAR BOUNDARY VALUE PROBLEMS

2010 ◽  
Vol 08 (03) ◽  
pp. 305-314 ◽  
Author(s):  
RADU PRECUP
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Positive Solutions ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problems

The existence of two positive solutions for a class of singular boundary value problems is established by means of a combination of the Leray–Schauder principle with techniques from critical point theory.

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