scholarly journals Nontrivial Solutions for Dirichlet Boundary Value Systems with the(p1,…,pn)-Laplacian

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shang-Kun Wang ◽  
Wen-Wu Pan
Keyword(s):  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Nontrivial Solutions

Using critical point theory due to Bonanno (2012), we prove the existence of at least one nontrivial solution for Dirichlet boundary value systems with the(p1,…,pn)-Laplacian.

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.

Existence of nontrivial solutions for boundary value problems of second-order discrete systems

2011 ◽  
Vol 61 (5) ◽  
Author(s):  
Xingyong Zhang ◽  
Xianhua Tang
Keyword(s):  
Boundary Value Problems ◽  
Critical Point ◽  
Critical Point Theory ◽  
Boundary Value ◽  
Discrete Systems ◽  
Point Theory ◽  
Second Order ◽  
Nontrivial Solutions ◽  
Solvability Conditions

AbstractBy making use of critical-point theory, some new solvability conditions for boundary value problems of second-order discrete systems with a parameter are obtained.

scholarly journals Existence of Nontrivial Solutions for Sixth-Order Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1852
Author(s):  
Gabriele Bonanno ◽  
Pasquale Candito ◽  
Donal O’Regan
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Critical Point ◽  
Nontrivial Solution ◽  
Critical Point Theory ◽  
Point Theory ◽  
Sixth Order ◽  
Nontrivial Solutions ◽  
Order Ordinary Differential Equation

We show the existence of at least one nontrivial solution for a nonlinear sixth-order ordinary differential equation is investigated. Our approach is based on critical point theory.

scholarly journals A variational approach for fractional boundary value systems depending on two parameters

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 517-530
Author(s):  
Ghasem Afrouzi ◽  
Samad Kolagar ◽  
Armin Hadjian ◽  
Jiafa Xu
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variational Approach ◽  
Boundary Value ◽  
Point Theory ◽  
Value Systems ◽  
Infinitely Many Solutions ◽  
Two Parameters

In this paper, we prove the existence of infinitely many solutions to nonlinear fractional boundary value systems, depending on two real parameters. The approach is based on critical point theory and variational methods. We also give an example to illustrate the obtained results.

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 Nontrivial Solutions for a Class of p-Kirchhoff Dirichlet Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xian Hu ◽  
Yong-Yi Lan
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Variational Method ◽  
Critical Point ◽  
Critical Point Theory ◽  
Dirichlet Boundary ◽  
Mountain Pass Theorem ◽  
Point Theory ◽  
Nontrivial Solutions ◽  
Kirchhoff Type

This paper is devoted to the following p-Kirchhoff type of problems −a+b∫Ω∇updxΔpu=fx,u,x∈Ωu=0,x∈∂Ω with the Dirichlet boundary value. We show that the p-Kirchhoff type of problems has at least a nontrivial weak solution. The main tools are variational method, critical point theory, and mountain-pass theorem.

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