Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains

Xu, Dong; Wei, Yuanhong

doi:10.1016/j.na.2019.03.024

Cited by 13 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for any dimension N ≥ 1. In [23], Dong and Wei established the existence of radial solutions for the following nonlinear elliptic equations with gradient terms in annular domains:…”

Section: Introductionmentioning

confidence: 99%

Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain

Wang

Alzabut

Khuddush³

et al. 2023

Axioms

View full text Add to dashboard Cite

This work explores the possibility that iterative classes of elliptic equations have both single and coupled positive radial solutions. Our approach is based on using the well-known Guo–Krasnoselskii and Avery–Henderson fixed-point theorems in a Banach space. Furthermore, we utilize Rus’ theorem in a metric space, to prove the uniqueness of solutions for the problem. Examples are constructed for the sake of verification.

show abstract

“…for any dimension N ≥ 1. In [23], Dong and Wei established the existence of radial solutions for the following nonlinear elliptic equations with gradient terms in annular domains:…”

Section: Introductionmentioning

confidence: 99%

Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain

Wang

Alzabut

Khuddush³

et al. 2023

Axioms

View full text Add to dashboard Cite

show abstract

“…There are some works related to asymptotically linear problems, such as Jeanjean-Tanaka [8], Stuart-Zhou [10] for second order elliptic equation, Wei-Su [13] for non-local elliptic equation, and Wei [12] for fourth-order elliptic equation etc. For more applications of this problem, we refer to Girardi-Matzeu [7] for periodic solutions of Hamiltonian system and Dong-Wei [6] for radial solutions of elliptic equation etc.…”

Section: Introductionmentioning

confidence: 99%

Asymptotically linear and superlinear elliptic equations with gradient terms

Wei,

Tian

2020

ejde

Self Cite

View full text Add to dashboard Cite

In this article we establish the existence of solutions for elliptic problem involving a gradient term. To handle the so-called non-variational problem, we use a variational methods. We assume that the nonlinear term satisfies an asymptotically linear growth condition or a superlinear growth condition. We show the existence of at least one positive solution and one negative solution. For more information see https://ejde.math.txstate.edu/Volumes/2020/99/abstr.html

show abstract

“…Lair [10] has considered the necessary and sufficient conditions for the existence of the nonnegative entire large radial solution of the system (4). There are the further results in [1,2,4,5,6,7,11,12,17,18,19,26,27,32] and the references therein.…”

mentioning

confidence: 99%

Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator

Yang¹,

Wang²,

Agarwal³

et al. 2021

DCDS-S

View full text Add to dashboard Cite

In this paper, we study the positive solutions of the Schrödinger elliptic system div(G(|∇y| p−2)∇y) = b 1 (|x|)ψ(y) + h 1 (|x|)ϕ(z), x ∈ R n (n ≥ 3), div(G(|∇z| p−2)∇z) = b 2 (|x|)ψ(z) + h 2 (|x|)ϕ(y), x ∈ R n , where G is a nonlinear operator. By using the monotone iterative technique and Arzela-Ascoli theorem, we prove that the system has the positive entire bounded radial solutions. Then, we establish the results for the existence and nonexistence of the positive entire blow-up radial solutions for the nonlinear Schrödinger elliptic system involving a nonlinear operator. Finally, three examples are given to illustrate our results.

show abstract

Existence of radial solutions for nonlinear elliptic equations with gradient terms in annular domains

Cited by 13 publications

References 27 publications

Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain

Solvability of Iterative Classes of Nonlinear Elliptic Equations on an Exterior Domain

Asymptotically linear and superlinear elliptic equations with gradient terms

Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator

Contact Info

Product

Resources

About