scholarly journals Multiple solutions of impulsive Sturm–Liouville boundary value problem via lower and upper solutions and variational methods

2012 ◽  
Vol 387 (2) ◽  
pp. 475-489 ◽  
Author(s):  
Yu Tian ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Sturm Liouville

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 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 Existence of Multiple Solutions for Boundary Value Problem with One Dimensional p-Laplacian

2013 ◽  
Vol 54 (1) ◽  
pp. 153-163
Author(s):  
Boris Rudolf
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Growth Condition ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Lower And Upper Solutions ◽  
Existence Of A Solution ◽  
One Dimensional

Abstract The boundary value problem for a differential equation with one dimensional p-Laplacian is studied. The technique of lower and upper solutions is used. The existence of a solution for well ordered and unordered case as well as the existence of multiple solutions are proved. The growth condition is assumed only on a part of the nonlinearity.

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.

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