Infinitely many solutions to a quasilinear Schrödinger equation with a local sublinear term

Liang, Zhanping; Gao, Jinfeng; Li, Anran

doi:10.1016/j.aml.2018.09.015

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction2

Preliminary Results1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2024

Publication Types

Select...

Article6

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 7 publications

(3 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where H(t) t 0 h(s)ds. We require the change of variable [24][25][26][27] Frontiers in Physics frontiersin.org 02…”

Section: Preliminary Resultsmentioning

confidence: 99%

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Qiu

Cheng

et al. 2023

Front. Phys.

View full text Add to dashboard Cite

In this paper, we consider the non-existence and existence of solutions for a generalized quasilinear Schrödinger equation with a Kirchhoff-type perturbation. When the non-linearity h(u) shows critical or supercritical growth at infinity, the non-existence result for a quasilinear Schrödinger equation is proved via the Pohožaev identity. If h(u) shows asymptotically cubic growth at infinity, the existence of positive radial solutions for the quasilinear Schrödinger equation is obtained when b is large or equal to 0 and b is equal to 0 by the variational methods. Moreover, some properties are established as the parameter b tends to be 0.

show abstract

“…where H(t) t 0 h(s)ds. We require the change of variable [24][25][26][27] Frontiers in Physics frontiersin.org 02…”

Section: Preliminary Resultsmentioning

confidence: 99%

On the asymptotically cubic generalized quasilinear Schrödinger equations with a Kirchhoff-type perturbation

Qiu

Cheng

et al. 2023

Front. Phys.

View full text Add to dashboard Cite

show abstract

“…In [17], Zhou and Wu studied (1.1) with V (x) = 0 in a bounded domain. Liang, Gao and Li [10] treated a quasilinear Schrödinger equation with 0…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, without imposing any growth condition of g(x, u) at infinity with respect to u, the existence of infinitely many small solutions for the problem (1.1) 1250 Gui Bao and Tingzhi Cheng is obtained. Furthermore, unlike [10,17], the potential V in this paper is allowed to be sign-changing.…”

Section: Introductionmentioning

confidence: 99%