Solvability for a fractional p " role="presentation" style="position: relative;"> p p p -Laplacian equation in a bounded domain

AIMS Mathematics

article

Zhiwei Lv¹  Jiafa Xu²  Donal O'Regan³ 

[1] School of Sciences and Arts, Suqian University;School of Mathematical Sciences, Chongqing Normal University;School of Mathematical and Statistical Sciences, National University of Ireland

关键词: fractional $ p $-Laplacian equation;    weak solution;    topological degree;    fountain theorem;    $ (p-1) $-asymptotically linear;    Landesman-Lazer type condition;   

DOI  :  10.3934/math.2022731

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this paper we use the topological degree and the fountain theorem to study the existence of weak solutions for a fractional $ p $-Laplacian equation in a bounded domain. For the nonlinearity $ f $, we consider two situations: (1) the non-resonance case where $ f $ is $ (p-1) $-asymptotically linear at infinity; (2) the resonance case where $ f $ satisfies the Landesman-Lazer type condition.

【 授权许可】

CC BY