Existence and behavior of positive solution for a problem with discontinuous nonlinearity in $${\mathbb {R}}^{N}$$ via a nonsmooth penalization

Santos, Gelson G. dos; Figueiredo, Giovany M.; Nascimento, Rúbia G.

doi:10.1007/s00033-020-01296-7

Cited by 11 publications

(3 citation statements)

References 17 publications

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“…Moreover, if s = 1, we get the classic Laplacian. Some related results can be found in [21,39,40,41,42]. Notice that when s = 1, the problems like (1.1)…”

Section: Introduction and Main Resultsmentioning

confidence: 74%

The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities

Hammar

Allalou

Abbassi

et al. 2022

Cubo

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In this article, we use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional p(x)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent. RESUMENEn este artículo, usamos el grado topológico basado en la ecuación abstracta de Hammerstein para investigar la existencia de soluciones débiles para una clase de problemas elípticos de valor en la frontera de Dirichlet que involucran el operador p(x)-Laplaciano fraccional con no linealidades discontinuas. El marco funcional apropiado para estos problemas es el espacio de Sobolev fraccional con exponente variable.

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“…Moreover, if s = 1, we get the classic Laplacian. Some related results can be found in [21,39,40,41,42]. Notice that when s = 1, the problems like (1.1)…”

Section: Introduction and Main Resultsmentioning

confidence: 74%

The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities

Hammar

Allalou

Abbassi

et al. 2022

Cubo

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“…Our arguments were strongly influenced by [2], [9], [10], [11], [17], [18], [25], [31] and [36]. Below we list what we believe to be the main contributions of our paper.…”

Section: Introductionmentioning

confidence: 89%

Existence and concentration of ground state solutions for a class of subcritical, critical or supercritical problems with steep potential well

Costa,

Figueiredo

2023

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“…Moreover, many problems related to the Kirchhoff term have been studied by a number of authors by employing different techniques as the method of sub-supersolution, fixed point theory, variational methods, genus theory and approximation techniques. For obtain the existence results, we mention the works [7,18,21,34].…”

Section: Introduction and Hypothesesmentioning

confidence: 99%

A weak solution to a Kirkoff type problem with discontinuous nonlinearities

Kassidi,

Melliani,

Sabiry

et al. 2023

BUT_Series_III

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Existence and behavior of positive solution for a problem with discontinuous nonlinearity in $${\mathbb {R}}^{N}$$ via a nonsmooth penalization

Cited by 11 publications

References 17 publications

The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities

The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities

Existence and concentration of ground state solutions for a class of subcritical, critical or supercritical problems with steep potential well

A weak solution to a Kirkoff type problem with discontinuous nonlinearities

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