Solvability for a fractional $ p $-Laplacian equation in a bounded domain-Reference-Cited by-同舟云学术

Solvability for a fractional $ p $-Laplacian equation in a bounded domain

Published:2022 Issue:7 Volume:7 Page:13258-13270
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Lv Zhiwei¹,Xu Jiafa²,O'Regan Donal³

Affiliation:

1. School of Sciences and Arts, Suqian University, Suqian 223800, China

2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China

3. School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference30 articles.

1. F. Browder, Fixed point theory and nonlinear problems, Bull. Amer. Math. Soc., 9 (1983), 1–39. http://dx.doi.org/10.1090/S0273-0979-1983-15153-4

2. K. Du, R. Peng, N. Sun, The role of protection zone on species spreading governed by a reaction-diffusion model with strong Allee effect, J. Differ. Equations, 266 (2019), 7327–7356. http://dx.doi.org/10.1016/j.jde.2018.11.035

3. G. Franzina, G. Palatucci, Fractional $p$-eigenvalues, Riv. Math. Univ. Parma., 5 (2014), 373–386.

4. B. Ge, Y. Cui, L. Sun, M. Ferrara, The positive solutions to a quasi-linear problem of fractional $p$-Laplacian type without the Ambrosetti-Rabinowitz condition, Positivity, 22 (2018), 873–895. http://dx.doi.org/10.1007/s11117-018-0551-z

5. K. Ho, K. Perera, I. Sim, M. Squassina, A note on fractional $p$-Laplacian problems with singular weights, J. Fixed Point Theory Appl., 19 (2017), 157–173. http://dx.doi.org/10.1007/s11784-016-0344-6

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Revisiting generalized Caputo derivatives in the context of two-point boundary value problems with the p-Laplacian operator at resonance;Boundary Value Problems;2023-06-15