Solutions to periodic BVP for second order impulsive differential equation with a p-Laplacian operator

2021 ◽  
Vol 15 (4) ◽  
pp. 193-203
Author(s):  
Zheng Huang ◽  
Ling Zhang ◽  
Jingli Xie
Keyword(s):  
Differential Equation ◽  
Impulsive Differential Equation ◽  
Second Order ◽  
Laplacian Operator

scholarly journals Semi-nonoscillation intervals and sign-constancy of Green’s functions of two-point impulsive boundary-value problems

2021 ◽  
Vol 73 (7) ◽  
pp. 887-901
Author(s):  
A. Domoshnitsky ◽  
Iu. Mizgireva ◽  
V. Raichik
Keyword(s):  
Differential Equation ◽  
Boundary Value Problems ◽  
Impulsive Differential Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Value ◽  
Homogeneous Equation ◽  
Second Order ◽  
Differential Inequalities ◽  
Impulsive Boundary Value Problems

UDC 517.9 We consider the second order impulsive differential equation with delays    where for  In this paper, we obtain the conditions of semi-nonoscillation for the corresponding homogeneous equation on the interval   Using these results, we formulate theorems on sign-constancy of Green's functions for two-point impulsive boundary-value problems in terms of differential inequalities. 

Variational methods to the p-Laplacian type nonlinear fractional order impulsive differential equations with Sturm-Liouville boundary-value problem

2021 ◽  
Vol 24 (4) ◽  
pp. 1069-1093
Author(s):  
Dandan Min ◽  
Fangqi Chen
Keyword(s):  
Differential Equation ◽  
Variational Methods ◽  
Impulsive Differential Equation ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Laplacian Operator ◽  
Infinitely Many Solutions ◽  
Critical Point Theorem ◽  
Sturm Liouville ◽  
New Criteria

Abstract In this paper, we consider a class of nonlinear fractional impulsive differential equation involving Sturm-Liouville boundary-value conditions and p-Laplacian operator. By making use of critical point theorem and variational methods, some new criteria are given to guarantee that the considered problem has infinitely many solutions. Our results extend some recent results and the conditions of assumptions are easily verified. Finally, an example is given as an application of our fundamental results.

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