Variational Methods in Differential Equations

2014 ◽  
pp. 171-186
Author(s):  
Michiaki Onodera
Keyword(s):  
Differential Equations ◽  
Variational Methods

scholarly journals Multiple Solutions of Second-Order Damped Impulsive Differential Equations with Mixed Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jian Liu ◽  
Lizhao Yan
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Mixed Boundary ◽  
Impulsive Differential Equations ◽  
Mixed Boundary Conditions ◽  
Second Order ◽  
Multiplicity Of Solutions

We use variational methods to investigate the solutions of damped impulsive differential equations with mixed boundary conditions. The conditions for the multiplicity of solutions are established. The main results are also demonstrated with examples.

scholarly journals EXISTENCE OF 3-WEAK SOLUTIONS FOR A NEW CLASS OF AN OVERDETERMINED SYSTEM OF FRACTIONAL PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040036 ◽  
Author(s):  
SALAH BOULAARAS ◽  
RAFIK GUEFAIFIA ◽  
ASMA ALHARBI ◽  
BAHRI CHERIF
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Critical Point ◽  
Differential System ◽  
Point Theorem ◽  
Weak Solutions ◽  
Overdetermined System ◽  
Critical Point Theorem ◽  
New Class

The paper deals with the existence of three different weak solutions of [Formula: see text] -Laplacian fractional for an overdetermined nonlinear fractional partial Fredholm–Volterra integro-differential system by using variational methods combined with a critical point theorem due to Bonanno and Marano.

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.

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