Existence of infinitely many positive radial solutions for an iterative system of nonlinear elliptic equations on an exterior domain

Khuddush, Mahammad; Prasad, K. Venkatesh

doi:10.1007/s13370-022-01027-3

Cited by 3 publications

(2 citation statements)

References 21 publications

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“…that is, d(Fz 1 , Fy 1 ) ≤ α 1 ρ(z 1 , y 1 ), (17) for some α 1 = α d 1 α 1 > 0 for all z 1 , y 1 ∈ X, this proves (14). Next, let z 1 , y 1 ∈ X, and from ( 13) and (17), we obtain d(Fz 1 , Fy 1 ) ≤ α 1 ρ(z 1 , y 1 ) ≤ α 1 d(z 1 , y 1 ).…”

Section: Uniqueness Of Positive Radial Solutionmentioning

confidence: 99%

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

Wang

Alzabut

Khuddush³

et al. 2023

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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.

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Section: Uniqueness Of Positive Radial Solutionmentioning

confidence: 99%

“…In [10], again for d = 2, Ali-Shivaji discussed the existence of multiple positive solutions for λ >> 1 when F(0) = 0 = F (0) for β ∈ {1, 2}. In addition, in [11][12][13][14][15][16][17][18][19][20], relevant references to the most recent works on (1) can be found. Next, we quote some recent works on elliptic equations.…”

Section: Introductionmentioning

confidence: 99%

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

Wang

Alzabut

Khuddush³

et al. 2023

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Infinite-time blowup and global solutions for a semilinear Klein–Gordan equation with logarithmic nonlinearity

Rao,

Khuddush,

Singh

et al. 2023

Applied Mathematics in Science and Engineering

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Existence and uniqueness of radial solution for the elliptic equation system in an annulus

Wang¹,

2023

MATH

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<abstract>This article discusses the existence and uniqueness of radial solution for the elliptic equation system <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left \{ \begin{array}{ll} -\triangle u = f(|x|, \ u, \ v, \ |\nabla u|), \; \; x\in \Omega, \\[10pt] -\triangle v = g(|x|, \ u, \ v, \ |\nabla v|), \; \; x\in \Omega, \\[10pt] u|_{\partial \Omega} = 0, \; v|_{\partial \Omega} = 0, \end{array} \right. $\end{document} </tex-math></disp-formula> where $ \Omega = \{x\in \mathbb{R}^{N}:\; r_1 < |x| < r_2\}, \; N\ge 3, \; f, \; g:[r_1, \; r_2]\times \mathbb{R}\times \mathbb{R}\times \mathbb{R}^+\to \mathbb{R} $ are continuous. Due to the appearance of the gradient term in the nonlinearity, the equation system has no variational structure and the variational method cannot be applied to it directly. We will give the correlation conditions of $ f $ and $ g $, that is, $ f $ and $ g $ are superlinear or sublinear, and prove the existence and uniqueness of radial solutions by using Leray-Schauder fixed point theorem.</abstract>

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Existence of infinitely many positive radial solutions for an iterative system of nonlinear elliptic equations on an exterior domain

Cited by 3 publications

References 21 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

Infinite-time blowup and global solutions for a semilinear Klein–Gordan equation with logarithmic nonlinearity

Existence and uniqueness of radial solution for the elliptic equation system in an annulus

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