Multiplicity of positive solutions for a singular and critical problem

Giacomoni, Jacques; Saoudi, Kamel

doi:10.1016/j.na.2009.02.087

Cited by 65 publications

(24 citation statements)

References 15 publications

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“…Here the authors have proved the existence of two positive solutions. Similar type of results to obtain existence and multiplicity (finitely many) of solutions can be found in [17,18,19,20,21] and the references therein. Recently, Saoudi et al [20] considered a fractional p-Laplacian version of (1.1) and proved the existence of two solutions to it by using a variational methods.…”

Section: Introductionsupporting

confidence: 60%

Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

Ghosh

Choudhuri

2019

Positivity

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Section: Introductionsupporting

confidence: 60%

Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

Ghosh

Choudhuri

2019

Positivity

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“…The same discontinuity at infinitum appears in the context of singular phenomena in nonlinear elliptic problems [1,2,9,17,34].…”

Section: Green's Identitiesmentioning

confidence: 80%

Spacetime singularity, singular bounds and compactness for solutions of the Poisson's equation

Aranda¹

2015

Cubo

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A black hole is a spacetime region in whose interior lies a structure known as a spacetime singularity whose scientific description is profoundly elusive, and which depends upon the still missing theory of quantum gravity. Using the classical weak comparison principle we are able to obtain new bounds, compactness results and concentration phenomena in the theory of Newtonian potentials of distributions with compact support which gives a suitable mathematical theory of spacetime singularity. We derive a rigorous renormalization of the Newtonian gravity law using nonlinear functional analysis and we have a solid set of astronomical observations supporting our new equation. This general setting introduces a new kind of ill posed problem with a very simple physical interpretation. RESUMENUn hoyo negro es una región espacio-temporal en cuyo interior hay una estructura llamada singularidad espacio-temporal cuya descripción científica es difícil de encontrar, y que depende de la aún inexistente teoría de la gravedad cuántica. Usando el clásico principio de comparación débil, aquí probamos nuevas cotas, resultados de compacidad y fenómenos de concentración en la teoría de potenciales Newtonianos de distribuciones de soporte compacto, que dan una teoría matemática adecuada de la singularidad espacio-temporal. Derivamos una rigurosa renormalización de la ley de gravitación Newtoniana usando análisis funcional no lineal y tenemos un contundente conjunto de datos de observaciones astronómicas que apoyan nuestra nueva ecuación. Este marco general introduce una nueva forma de problema mal-puesto con una interpretación física muy simple.

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“…Historically, problem (P λ ) with M(x) = I has quite an extensive literature (see [3,4,5,6,7,8,9,10,11,12,13,14,15,16]) with their references therein. It seems that problem (P λ ), has attracted less attention.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

A multiplicity result for a singular problem with subcritical nonlinearities

2017

J. Nonlinear Funct. Anal.

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Multiplicity of positive solutions for a singular and critical problem

Cited by 65 publications

References 15 publications

Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

Spacetime singularity, singular bounds and compactness for solutions of the Poisson's equation

A multiplicity result for a singular problem with subcritical nonlinearities

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