Positive radial solutions for a boundary value problem associated to a system of elliptic equations with semipositone nonlinearities

Guo, Limin; Xu, Jiafa; O’Regan, Donal

doi:10.3934/math.2023053

MATH

2023

DOI: 10.3934/math.2023053

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Positive radial solutions for a boundary value problem associated to a system of elliptic equations with semipositone nonlinearities

Limin Guo

Jiafa Xu

Donal O’Regan

Abstract: <abstract>In this paper we use the fixed point index theory to study the existence of positive radial solutions for a system of boundary value problems with semipositone second order elliptic equations. Some appropriate concave and convex functions are utilized to characterize coupling behaviors of our nonlinearities.</abstract>

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

Wang¹,

2023

MATH

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Positive radial solutions for a boundary value problem associated to a system of elliptic equations with semipositone nonlinearities

Cited by 1 publication

References 31 publications

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

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

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