scholarly journals An Application of Coincidence Degree Continuation Theorem in Existence of Solutions of Impulsive Differential Equations

1996 ◽  
Vol 197 (3) ◽  
pp. 875-889 ◽  
Author(s):  
Yujun Dong ◽  
Erxin Zhou
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Impulsive Differential Equations ◽  
Continuation Theorem

scholarly journals Some Antiperiodic Boundary Value Problem for Nonlinear Fractional Impulsive Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Xianghu Liu ◽  
Yanfang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Existence Of Solutions ◽  
Integral Formula ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Uniqueness Of Solutions ◽  
Liouville Fractional Derivative

This paper is concerned with the sufficient conditions for the existence of solutions for a class of generalized antiperiodic boundary value problem for nonlinear fractional impulsive differential equations involving the Riemann-Liouville fractional derivative. Firstly, we introduce the fractional calculus and give the generalized R-L fractional integral formula of R-L fractional derivative involving impulsive. Secondly, the sufficient condition for the existence and uniqueness of solutions is presented. Finally, we give some examples to illustrate our main results.

scholarly journals Existence of solutions for first-order Hamiltonian random impulsive differential equations with Dirichlet boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yu Guo ◽  
Xiao-Bao Shu ◽  
Qianbao Yin
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Energy Functional ◽  
Dirichlet Boundary Conditions ◽  
Mountain Pass Lemma ◽  
First Order

<p style='text-indent:20px;'>In this paper, we study the sufficient conditions for the existence of solutions of first-order Hamiltonian random impulsive differential equations under Dirichlet boundary value conditions. By using the variational method, we first obtain the corresponding energy functional. And by using Legendre transformation, we obtain the conjugation of the functional. Then the existence of critical point is obtained by mountain pass lemma. Finally, we assert that the critical point of the energy functional is the mild solution of the first order Hamiltonian random impulsive differential equation. Finally, an example is presented to illustrate the feasibility and effectiveness of our results.</p>

scholarly journals The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yumei Zou ◽  
Lishan Liu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
At Resonance ◽  
Fractional Differential

A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of resonance.

scholarly journals An Existence Result for Second-Order Impulsive Differential Equations with Nonlocal Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Meili Li ◽  
Haiqiang Liu
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Impulsive Differential Equations ◽  
Second Order

The Leray-Schauder alternative is used to investigate the existence of solutions for second-order impulsive differential equations with nonlocal conditions in Banach spaces. The results improve some recent results.

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