Variational approach to p -Laplacian fractional differential equations with instantaneous and non-instantaneous impulses

AIMS Mathematics

article

Zhilin Li¹  Guoping Chen²  Weiwei Long¹  Xinyuan Pan¹ 

[1] College of Mathematics and Statistics, Jishou University;School of Civil Engineering and Architecture, Jishou University

关键词: fractional differential equation;    impulsive effects;    p -Laplacian operator;    variational approach;    mountain pass lemma;   

DOI  :  10.3934/math.2022933

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper, we examine the existence of solutions of p -Laplacian fractional differential equations with instantaneous and non-instantaneous impulses. New criteria guaranteeing the existence of infinitely many solutions are established for the considered problem. The problem is reduced to an equivalent form such that the weak solutions of the problem are defined as the critical points of an energy functional. The main result of the present work is established by using a variational approach and a mountain pass lemma. Finally, an example is given to illustrate our main result.

【 授权许可】

CC BY