Applications of variational methods to Sturm-Liouville boundary-value problem for fourth-order impulsive differential equations

2013 ◽  
Vol 37 (1) ◽  
pp. 95-105 ◽  
Author(s):  
Yu Tian ◽  
Xianbin Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Sturm Liouville

scholarly journals APPLICATIONS OF VARIATIONAL METHODS TO BOUNDARY-VALUE PROBLEM FOR IMPULSIVE DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 51 (2) ◽  
pp. 509-527 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Variational Methods ◽  
Positive Solutions ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Impulsive Effects ◽  
Differential Inequalities ◽  
Existence Of Positive Solutions ◽  
Sturm Liouville

AbstractIn this paper, we investigate the existence of positive solutions to a second-order Sturm–Liouville boundary-value problem with impulsive effects. The ideas involve differential inequalities and variational methods.

scholarly journals The Solutions of Sturm-Liouville Boundary-Value Problem for Fourth-Order Impulsive Differential Equation via Variational Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Yu Tian ◽  
Dongpo Sun
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Multiple Solutions ◽  
Impulsive Differential Equation ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Sturm Liouville ◽  
Main Ideas

The Sturm-Liouville boundary-value problem for fourth-order impulsive differential equations is studied. The existence results for one solution and multiple solutions are obtained. The main ideas involve variational methods and three critical points theory.

scholarly journals Existence of Solutions for Sturm-Liouville Boundary Value Problem of Impulsive Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Hong-Rui Sun ◽  
Ya-Ning Li ◽  
Juan J. Nieto ◽  
Qing Tang
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Boundary Value Problem ◽  
Multiple Solutions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Critical Point Theorems ◽  
Sturm Liouville ◽  
Existence Criteria

This paper is concerned with the existence of solutions for Sturm-Liouville boundary value problem of a class of second-order impulsive differential equations, under different assumptions on the nonlinearity and impulsive functions, existence criteria of single and multiple solutions are established. The main tools are variational method and critical point theorems. Some examples are also given to illustrate the main results.

EXISTENCE AND UNIQUENESS OF WEAK AND CLASSICAL SOLUTIONS FOR A FOURTH-ORDER SEMILINEAR BOUNDARY VALUE PROBLEM

2019 ◽  
Vol 61 (3) ◽  
pp. 305-319
Author(s):  
CRISTIAN-PAUL DANET
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Fourth Order ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Classical Solutions ◽  
Maximum Principles ◽  
Uniqueness Results

This paper is concerned with the problem of existence and uniqueness of weak and classical solutions for a fourth-order semilinear boundary value problem. The existence and uniqueness for weak solutions follows from standard variational methods, while similar uniqueness results for classical solutions are derived using maximum principles.

Factorization Ladders and Eigenfunctions

1949 ◽  
Vol 1 (4) ◽  
pp. 379-396 ◽  
Author(s):  
G. F. D. Duff
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Integral Equations ◽  
Manufacturing Process ◽  
Boundary Value ◽  
Factorization Method ◽  
Sturm Liouville ◽  
The Subject

The eigenfunctions of a boundary value problem are characterized by two quite distinct properties. They are solutions of ordinary differential equations, and they satisfy prescribed boundary conditions. It is a definite advantage to combine these two requirements into a single problem expressed by a unified formula. The use of integral equations is an example in point. The subject of this paper, namely the Schrödinger-Infeld Factorization Method, which is applicable to certain restricted. Sturm-Liouville problems, is based upon another combination of the two properties. The Factorization Method prescribes a manufacturing process.

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