Multiplicity of positive weak solutions to subcritical singular elliptic Dirichlet problems

Godoy, T.; Guerin, A.

doi:10.14232/ejqtde.2017.1.100

Cited by 9 publications

(2 citation statements)

References 32 publications

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“…were studied in [9] in the case when m is a nonnegative and nonidentically zero function belonging to L ∞ (Ω) , and b is a singular potential of the form b = av −α−1 , where:…”

Section: Introductionmentioning

confidence: 99%

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Principal eigenvalues of elliptic problems with singular potential and bounded weight function

Godoy

2023

Constructive Mathematical Analysis

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Let $\Omega$ be a bounded domain in $\mathbb{R}^{n}$ with $C^{0,1}$ boundary, and let $d_{\Omega}:\Omega\rightarrow\mathbb{R}$ be the distance function $d_{\Omega}\left( x\right) :=dist\left( x,\partial\Omega\right) .$ Our aim in this paper is to study the existence and properties of principal eigenvalues of self-adjoint elliptic operators with weight function and singular potential, whose model problem is $-\Delta u+bu=\lambda mu$ in $\Omega,$ $u=0$ on $\partial\Omega,$ $u>0$ in $\Omega,$ where $b:\Omega \rightarrow\mathbb{R}$ is a nonnegative function such that $d_{\Omega}^{2}b\in L^{\infty}\left( \Omega\right) ,$ $m:\Omega\rightarrow\mathbb{R}$ is a nonidentically zero function in $L^{\infty}\left( \Omega\right) $ that may change sign, and the solutions are understood in weak sense.

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“…were studied in [9] in the case when m is a nonnegative and nonidentically zero function belonging to L ∞ (Ω) , and b is a singular potential of the form b = av −α−1 , where:…”

Section: Introductionmentioning

confidence: 99%

“…Under these assumptions, Lemmas 4.3 and 4.4 in [9] state the existence of a positive principal eigenvalue for problem (1.7), and a maximum principle with weight.…”

Section: Introductionmentioning

confidence: 99%

Principal eigenvalues of elliptic problems with singular potential and bounded weight function

Godoy

2023

Constructive Mathematical Analysis

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The uniqueness of some singular Kirchhoff equations with non-homogeneous material

Yan,

O’Regan,

Agarwal

2023

Indian J Pure Appl Math

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Elliptic bifurcation problems that are singular in the dependent and in the independent variables

Godoy

Guerin

2019

Complex Variables and Elliptic Equations

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Multiplicity of positive weak solutions to subcritical singular elliptic Dirichlet problems

Cited by 9 publications

References 32 publications

Principal eigenvalues of elliptic problems with singular potential and bounded weight function

Principal eigenvalues of elliptic problems with singular potential and bounded weight function

The uniqueness of some singular Kirchhoff equations with non-homogeneous material

Elliptic bifurcation problems that are singular in the dependent and in the independent variables

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