scholarly journals Multiple Solutions for Nonlinear Navier Boundary Systems Involving(p1(x),…,pn(x))-Biharmonic Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Variable Exponent ◽  
Multiplicity Of Solutions ◽  
Biharmonic Problem ◽  
Existence And Multiplicity ◽  
Variable Exponent Sobolev Spaces

We improve some results on the existence and multiplicity of solutions for the(p1(x),…,pn(x))-biharmonic system. Our main results are new. Our approach is based on general variational principle and the theory of the variable exponent Sobolev spaces.

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

scholarly journals Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

2017 ◽  
Vol 3 (1) ◽  
pp. 70-82
Author(s):  
A. Ahmed ◽  
M.S.B. Elemine Vall ◽  
A. Touzani
Keyword(s):  
Variational Principle ◽  
Critical Point ◽  
Neumann Problem ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Elliptic Systems ◽  
Subject Classification ◽  
Infinitely Many Solutions ◽  
Variable Exponent Sobolev Spaces ◽  
The Neumann Problem

Abstract In this paper, we prove the existence of in finitely many solutions for the following system by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle and the theory of the anisotropic variable exponent Sobolev spaces 2010 Mathematics Subject Classification. 35K05 - 35K55.

scholarly journals Multiple Solutions for a Nonlocal Elliptic Problem Involving p x , q x -Biharmonic Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Qi Zhang ◽  
Qing Miao
Keyword(s):  
Variational Principle ◽  
Elliptic Problem ◽  
Multiple Solutions ◽  
Sufficient Conditions ◽  
Biharmonic Operator ◽  
Type Problem ◽  
Navier Boundary Conditions ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Kirchhoff Type Problem

In this paper, using the variational principle, the existence and multiplicity of solutions for p x , q x -Kirchhoff type problem with Navier boundary conditions are proved. At the same time, the sufficient conditions for the multiplicity of solutions are obtained.

scholarly journals Existence and multiplicity results for a class of Kirchho type problems involving the p(x)-biharmonic operator

2017 ◽  
Vol 37 (2) ◽  
pp. 23-33
Author(s):  
Omar Darhouche
Keyword(s):  
Variational Method ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Nonlocal Problem ◽  
Biharmonic Operator ◽  
Technical Approach ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Variable Exponent Sobolev Spaces ◽  
Direct Variational Method

The aim of this paper is to establish the existence and multiplicity of solutions for a class of nonlocal problem involving the p(x)-biharmonic operator. Our technical approach is based on direct variational method and the theory of variable exponent Sobolev spaces.

scholarly journals Infinitely many solutions for a nonlinear Navier boundary systems involving $(p(x),q(x))$-biharmonic

2014 ◽  
Vol 33 (1) ◽  
pp. 155
Author(s):  
Mostafa Allaoui ◽  
Abdel Rachid El Amrouss ◽  
Anass Ourraoui
Keyword(s):  
Variational Principle ◽  
Sobolev Spaces ◽  
Variable Exponent ◽  
Type System ◽  
Infinitely Many Solutions ◽  
Variable Exponent Sobolev Spaces

In this article, we study the following $(p(x),q(x))$-biharmonic type system \begin{gather*} \Delta(|\Delta u|^{p(x)-2}\Delta u)=\lambda F_u(x,u,v)\quad\text{in }\Omega,\\ \Delta(|\Delta v|^{q(x)-2}\Delta v)=\lambda F_v(x,u,v)\quad\text{in }\Omega,\\ u=v=\Delta u=\Delta v=0\quad  \text{on }\partial\Omega. \end{gather*} We prove the existence of infinitely many solutions of the problem byapplying a general variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces.

scholarly journals Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Heidari ◽  
A. Razani
Keyword(s):  
Variational Methods ◽  
Sobolev Spaces ◽  
Multiple Solutions ◽  
Elliptic Systems ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Quasilinear Elliptic Systems ◽  
Quasilinear Elliptic

AbstractIn this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parameters such that the problem admits multiple solutions. Our approach is based on variational methods.

scholarly journals Nonlocal Variational Principles with Variable Growth

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Yongqiang Fu ◽  
Miaomiao Yang
Keyword(s):  
Sobolev Spaces ◽  
Lower Semicontinuity ◽  
Variable Exponent ◽  
Variational Principles ◽  
Young Measures ◽  
Bounded Set ◽  
Weak Lower Semicontinuity ◽  
Variable Exponent Sobolev Spaces ◽  
Regular Open

This paper is concerned with the functionalJdefined byJ(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, whereΩ⊂ℝNis a regular open bounded set andWis a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ.

Sign in / Sign up

Export Citation Format

Share Document