scholarly journals An Application of Variant Fountain Theorems to a Class of Impulsive Differential Equations with Dirichlet Boundary Value Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Liu Yang
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Classical Solutions ◽  
Boundary Value Condition ◽  
Fountain Theorems ◽  
Variant Fountain Theorems

We consider the existence of infinitely many classical solutions to a class of impulsive differential equations with Dirichlet boundary value condition. Our main tools are based on variant fountain theorems and variational method. We study the case in which the nonlinearity is sublinear. Some recent results are extended and improved.

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.

A variational approach for boundary value problems for impulsive fractional differential equations

2018 ◽  
Vol 21 (6) ◽  
pp. 1565-1584 ◽  
Author(s):  
Ghasem A. Afrouzi ◽  
Armin Hadjian
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Classical Solutions ◽  
Oscillatory Behaviour ◽  
Impulsive Fractional Differential Equations ◽  
Distinct Sequence ◽  
Fractional Differential ◽  
Critical Point Result

Abstract By using an abstract critical point result for differentiable and parametric functionals due to B. Ricceri, we establish the existence of infinitely many classical solutions for fractional differential equations subject to boundary value conditions and impulses. More precisely, we determine some intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable oscillatory behaviour at infinity, or a pairwise distinct sequence of solutions that strongly converges to zero if a similar behaviour occurs at zero. No symmetric condition on the nonlinear term is assumed. Two examples are then given.

scholarly journals Infinite Boundary Value Problems for Second-Order Nonlinear Impulsive Differential Equations with Supremum

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Piao-Piao Shi ◽  
Wen-Xia Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Solution Method ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Comparison Result ◽  
Upper Solution ◽  
Lower And Upper Solution

We investigate the infinite boundary value problems for second-order impulsive differential equations with supremum by establishing a new comparison result and using the lower and upper solution method, and obtain the existence results for their maximal and minimal solutions.

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