Critical point theory on convex subsets with applications in differential equations and analysis

2020 ◽  
Vol 141 ◽  
pp. 266-315 ◽  
Author(s):  
Abbas Moameni
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Convex Subsets

Existence of solutions for nonlinear fractional order p-Laplacian differential equations via critical point theory

2019 ◽  
Vol 22 (4) ◽  
pp. 945-967
Author(s):  
Nemat Nyamoradi ◽  
Stepan Tersian
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Fractional Order ◽  
Critical Point Theory ◽  
Existence Of Solutions ◽  
Point Theory ◽  
Fractional Boundary Value Problem ◽  
New Criteria

Abstract In this paper, we study the existence of solutions for a class of p-Laplacian fractional boundary value problem. We give some new criteria for the existence of solutions of considered problem. Critical point theory and variational method are applied.

The Applications of Critical-Point Theory to Discontinuous Fractional-Order Differential Equations

2017 ◽  
Vol 60 (4) ◽  
pp. 1021-1051 ◽  
Author(s):  
Yu Tian ◽  
Juan J. Nieto
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Fractional Integrals ◽  
Fractional Order Differential Equations ◽  
Variational Structure ◽  
Sturm Liouville ◽  
Left And Right ◽  
Fractional Equation

AbstractWe consider a fractional equation involving the left and right Riemann–Liouville fractional integrals and with Sturm–Liouville boundary-value conditions. We establish the variational structure of the problem and, by using critical-point theory, the existence of an unbounded sequence of solutions is obtained.

Variational perturbative methods and bifurcation of bound states from the essential spectrum

1998 ◽  
Vol 128 (6) ◽  
pp. 1131-1161 ◽  
Author(s):  
Antonio Ambrosetti ◽  
Marino Badiale
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Essential Spectrum ◽  
Critical Point Theory ◽  
Bound States ◽  
Point Theory ◽  
Perturbative Methods ◽  
Elliptic Differential Equations ◽  
Perturbative Method

This paper consists of two main parts. The first deals with a perturbative method in critical point theory and can be seen as the generalisation and completion of some earlier results. The second part is concerned with applications of the abstract setup to the existence of bound states of a class of elliptic differential equations that branch off from the infimum of the essential spectrum.

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 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 Periodic Solutions for Second-Order Ordinary Differential Equations with Linear Nonlinearity

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Xiaohong Hu ◽  
Dabin Wang ◽  
Changyou Wang
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Critical Point ◽  
Periodic Solutions ◽  
Critical Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Minimax Methods ◽  
Existence Of Periodic Solutions

By using minimax methods in critical point theory, we obtain the existence of periodic solutions for second-order ordinary differential equations with linear nonlinearity.

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