scholarly journals On a bi-nonlocal fourth order elliptic problem

2021 ◽  
Vol 40 (1) ◽  
pp. 239-253
Author(s):  
F. Jaafri ◽  
A. Ayoujil ◽  
M. Berrajaa
Keyword(s):  
Boundary Condition ◽  
Weak Solution ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Critical Point Theory ◽  
Point Theory ◽  
Navier Boundary Condition ◽  
Order Elliptic Problem

This paper is aiming at obtaining weak solution for a bi-nonlocal fourth order elliptic problem with Navier boundary condition. Our approach is based on variational methods and critical point theory.

scholarly journals Infinitely Many Homoclinic Solutions for Nonperiodic Fourth Order Differential Equations with General Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Point Theory ◽  
Homoclinic Solutions

We investigate a class of nonperiodic fourth order differential equations with general potentials. By using variational methods and genus properties in critical point theory, we obtain that such equations possess infinitely homoclinic solutions.

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 Infinitely many solutions for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions

2019 ◽  
Vol 38 (4) ◽  
pp. 71-96 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Anderson Luis Albuquerque de Araujo ◽  
Amjad Salari
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Critical Point Theory ◽  
Variable Exponent ◽  
Point Theory ◽  
Infinitely Many Solutions ◽  
Nonlocal Problems ◽  
Multiplicity Results

In this article we will provide new multiplicity results of the solutions for nonlocal problems with variable exponent and nonhomogeneous Neumann conditions. We investigate the existence of infinitely many solutions for perturbed nonlocal problems with variable exponent and nonhomogeneous Neumann conditions. The approach is based on variational methods and critical point theory.

scholarly journals Periodic Solutions for Semilinear Fourth-Order Differential Inclusions via Nonsmooth Critical Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bian-Xia Yang ◽  
Hong-Rui Sun
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Nonsmooth Critical Point Theory ◽  
Critical Point Theorem ◽  
Related Literature ◽  
Nonsmooth Critical Point

Three periodic solutions with prescribed wavelength for a class of semilinear fourth-order differential inclusions are obtained by using a nonsmooth version critical point theorem. Some results of previous related literature are extended.

scholarly journals Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xiaofang Meng ◽  
Yongkun Li
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Hamiltonian Systems ◽  
Time Scales ◽  
Critical Point Theory ◽  
Point Theory ◽  
Singular Hamiltonian Systems ◽  
Existence Of Periodic Solutions

We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory.

scholarly journals Properties of the extremal solution for a fourth-order elliptic problem

2012 ◽  
Vol 142 (5) ◽  
pp. 1051-1069 ◽  
Author(s):  
Baishun Lai ◽  
Zhuoran Du
Keyword(s):  
Weak Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Open Problem ◽  
Extremal Solution ◽  
Normal Vector ◽  
Unique Weak Solution ◽  
Unit Normal Vector ◽  
Order Elliptic Problem ◽  
Image Position

Let λ* > 0 denote the largest possible value of λ such that the systemhas a solution, where $\mathbb{B}$ is the unit ball in ℝn centred at the origin, p > 1 and n is the exterior unit normal vector. We show that for λ = λ* this problem possesses a unique weak solution u*, called the extremal solution. We prove that u* is singular when n ≥ 13 for p large enough and actually solve part of the open problem which Dávila et al. left unsolved.

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.

scholarly journals Multiple Periodic Solutions for a Class of Second-Order Neutral Impulsive Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Jingli Xie ◽  
Zhiguo Luo ◽  
Yuhua Zeng
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Functional Differential Equations ◽  
Point Theory ◽  
Second Order ◽  
Multiple Periodic Solutions ◽  
Functional Differential

In this paper, we study a class of second-order neutral impulsive functional differential equations. Under certain conditions, we establish the existence of multiple periodic solutions by means of critical point theory and variational methods. We propose an example to illustrate the applicability of our result.

scholarly journals Three Solutions for Fourth-Order Impulsive Differential Inclusions via Nonsmooth Critical Point Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Dongdong Gao ◽  
Jianli Li
Keyword(s):  
Critical Point ◽  
Fourth Order ◽  
Critical Point Theory ◽  
Differential Inclusions ◽  
Point Theory ◽  
Three Solutions ◽  
Nonsmooth Critical Point Theory ◽  
Critical Point Theorem ◽  
Impulsive Differential Inclusions ◽  
Nonsmooth Critical Point

An existence of at least three solutions for a fourth-order impulsive differential inclusion will be obtained by applying a nonsmooth version of a three-critical-point theorem. Our results generalize and improve some known results.

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