Analysis of positive radial solutions for singular superlinear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si27.svg"><mml:mi>p</mml:mi></mml:math>-Laplacian systems on the exterior of a ball

Son, Byungjae; Wang, Peiyong

doi:10.1016/j.na.2019.111657

Cited by 15 publications

(9 citation statements)

References 16 publications

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“…The authors considered the existence of a positive radial solution for small values of λ by applying degree theory and rescaling arguments. Always for the system case, the interested readers may refer to Felmer, Manásevich and Thelin [21], Hai [30,31], Hai and Shivaji [33], Son and Wang [46], Ahammou [1], Xiang, Zhang and Rȃdulescu [48]. On the basis of the above analysis, we extend the study of previous results in several ways.…”

Section: (3)mentioning

confidence: 55%

Positive solutions of singular multiparameter <i>p</i>-Laplacian elliptic systems

Feng¹,

Zhang²

2022

DCDS-B

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In this paper, by using the eigenvalue theory, the sub-supersolution method and the fixed point theory, we prove the existence, multiplicity, uniqueness, asymptotic behavior and approximation of positive solutions for singular multiparameter p-Laplacian elliptic systems on nonlinearities with separate variables or without separate variables. Various nonexistence results of positive solutions are also studied.

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Section: (3)mentioning

confidence: 55%

Positive solutions of singular multiparameter <i>p</i>-Laplacian elliptic systems

Feng¹,

Zhang²

2022

DCDS-B

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“…which have the same meaning as T . Next, we consider the existence results of system (S λ ,••• ,n ) by using a completely di erent method from that of [2,8,10,11,[14][15][16]20,21,29,30,32,35,36,40,41,46,49,50,[53][54][55]61], namely the eigenvalue theory:…”

Section: Preliminariesmentioning

confidence: 99%

“…At the same time, we notice that many authors have paid more attention to various of system problems, for example, see [2,10,[14][15][16]20,21,29,30,32,35,40,46,49,50]. Specially, Lair and Wood [36] analyzed the existence of entire positive solutions of system ∆u = p(|x|)v α , ∆v = q(|x|)u β ,…”

Section: Introductionmentioning

confidence: 99%

Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior

Feng

2020

Advances in Nonlinear Analysis

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In this paper, the equations and systems of Monge-Ampère with parameters are considered. We first show the uniqueness of of nontrivial radial convex solution of Monge-Ampère equations by using sharp estimates. Then we analyze the existence and nonexistence of nontrivial radial convex solutions to Monge-Ampère systems, which includes some new ingredients in the arguments. Furthermore, the asymptotic behavior of nontrivial radial convex solutions for Monge-Ampère systems is also considered. Finally, as an application, we obtain sufficient conditions for the existence of nontrivial radial convex solutions of the power-type system of Monge-Ampère equations.

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“…[3,4]). It is well known that the existence of positive radial solutions for these two kinds of problems has been studied by many scholars in different settings and many outstanding results have been obtained, see [1,30,21,17,36,34,18,19,16,23,10,22,6,7] and the references therein. In particularly, for the following elliptic problem…”

Section: Introductionmentioning

confidence: 99%

Radial solutions for a class of multiparameter singular k-Hessian systems

Ding,

Gao,

2023

Preprint

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This paper is devoted to studying the coupled system of multiparameter k-Hessian equations S_k(\mu(D^2u_1))=\lambda_1\rho_1(|x|)f_1(-u_1,-u_2) in B, S_k(\mu(D^2u_2))=\lambda_2\rho_2(|x|)f_2(-u_1,-u_2) in B, u_1=u_2=0 on \partial B, where B=\{x\in\mathbb{R}^n:|x|<1\}, \lambda_1,\lambda_2 are positive parameters, \rho_i\,(i=1,2) is singular near the boundary \partial B, f_i\,(i=1,2) satisfies a combined superlinear condition at \infty. Employing the fixed point theorem of Krasnosel'skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters \lambda_1,\lambda_2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case \lambda_1,\lambda_2\gg1. Mathematics Subject Classification (2010). 34B15, 34B18.

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Analysis of positive radial solutions for singular superlinear p-Laplacian systems on the exterior of a ball

Cited by 15 publications

References 16 publications

Positive solutions of singular multiparameter <i>p</i>-Laplacian elliptic systems

Positive solutions of singular multiparameter <i>p</i>-Laplacian elliptic systems

Convex solutions of Monge-Ampère equations and systems: Existence, uniqueness and asymptotic behavior

Radial solutions for a class of multiparameter singular k-Hessian systems

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