A Brezis–Nirenberg splitting approach for nonlocal fractional equations

Bisci, Giovanni Molica; Servadei, Raffaella

doi:10.1016/j.na.2014.10.025

Cited by 23 publications

(3 citation statements)

References 29 publications

(34 reference statements)

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“…Since problem (1) has a variational structure and its weak solutions can be obtained as critical points of the energy functional for problem (1), the existence and multiplicity of solutions have been widely investigated by variational methods, we refer the readers to [23,24,32,33,35,37,40] and the references therein. Generally speaking, when the energy functional possesses some symmetric properties, the classical multiple critical point theorems can be directly applied to find infinitely many solutions.…”

Section: Introduction and Main Results Consider The Following Problemmentioning

confidence: 99%

Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators

Zhang¹,

Tang²,

Chen³

2017

Communications on Pure &Amp; Applied Analysis

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In this paper, we consider the following perturbed nonlocal elliptic equation −L K u = λu + f (x, u) + g(x, u), x ∈ Ω, u = 0, x ∈ R N \ Ω, where Ω is a smooth bounded domain in R N , λ is a real parameter and g is a non-odd perturbation term. If f is odd in u and satisfies various superlinear growth conditions at infinity in u, infinitely many solutions are obtained in spite of the lack of the symmetry of this problem for any λ ∈ R. The results obtained in this paper may be seen as natural extensions of some classical theorems to the case of nonlocal operators. Moreover, the methods used in this paper can be also applied to obtain some new results for the classical Laplace equation with Dirichlet boundary conditions.

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Section: Introduction and Main Results Consider The Following Problemmentioning

confidence: 99%

Infinitely many solutions for a class of perturbed elliptic equations with nonlocal operators

Zhang¹,

Tang²,

Chen³

2017

Communications on Pure &Amp; Applied Analysis

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“…In the recent years many mathematicians have made efforts to apply the minimax methods ( [24]) such as the mountain pass theorem( [1]), the saddle point theorem( [24]) or other linking type of critical point theorems in the study of the non-local fractional Laplacian equations with different nonlinearities having subcritical or critical growth, see [3,14,21,22,25,26,27,28,30,31] and references therein. Both results and methods in dealing with the classical Laplace equations may be adapted to the non-local equations.…”

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confidence: 99%

Nontrivial solutions for the fractional Laplacian problems without asymptotic limits near both infinity and zero

Chen¹,

Su²

2021

DCDS-S

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“…See [24] and the references therein. In the recent years many mathematicians have made efforts to apply the minimax methods ( [25]) such as the mountain pass theorem [1], the saddle point theorem [25] or other linking type of critical point theorems in the study of the non-local fractional Laplacian equations with different nonlinearities having subcritical or critical growth, see [3,4,7,8,14,15,16,23,24,26,27,29,30,32,33] and references therein.…”

mentioning

confidence: 99%