On a class of fractional Schrödinger equations in with sign-changing potential

Souza, Manassés de; Araújo, Yane Lísley

doi:10.1080/00036811.2016.1276173

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…When V(x) is periodic, the existence of ground state solutions is investigated in [1,23,32,39]. For the case V(x) is allowed to be sign-changing, existence and multiplicity results of nontrivial solutions are given by [5,13,25].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

Li,

null,

Zhang

2023

ATA

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We study the existence of standing waves of fractional Schr ödinger equations with a potential term and a general nonlinear term:where s ∈ (0, 1), N > 2s is an integer and V(x) ≤ 0 is radial. More precisely, we investigate the minimizing problem with L 2 -constraint:Under general assumptions on the nonlinearity term f (u) and the potential term V(x), we prove that there exists a constant α 0 ≥ 0 such that E(α) can be achieved for all α > α 0 , and there is no global minimizer with respect to E(α) for all 0 < α < α 0 . Moreover, we propose some criteria determining α 0 = 0 or α 0 > 0.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Standing Waves of Fractional Schrödinger Equations with Potentials and General Nonlinearities

Li,

null,

Zhang

2023

ATA

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“…This equation is of particular interest in fractional quantum mechanics in the study of particles on stochastic fields modeled by Lévy processes. 4,5 Also, a detailed mathematical descriptions of Caffarell and Silvestre 6 can be found in the Appendix of Dávila et al 7 In recent years, with the aid of variational methods, the existence, nonexistence, and multiplicity results of various solutions for (1) have been extensively investigated, see, for instance, previous studies [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein. Furthermore, there have been enormous results considered the concentration property of solutions, see, for instance, previous studies 3,7,24,25 and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Ground state of solutions for a class of fractional Schrödinger equations with critical Sobolev exponent and steep potential well

Shao

Chen

2017

Math Methods in App Sciences

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In this paper, we study the following fractional Schrödinger equations:> 0, and are real parameter. 2 * is the critical Sobolev exponent. We prove a fractional Sobolev-Hardy inequality and use it together with concentration compact theory to get a ground state solution. Moreover, concentration behaviors of nontrivial solutions are obtained when the coefficient of the potential function tends to infinity.

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“…It is worthwhile to remark that in [2] and [25] the coercivity hypothesis is assumed on h in order to overcome the problem of lack of compactness, typical of elliptic problems defined in unbounded domains. For more works about the existence and multiplicity results to the equation (1) obtained by variational and topological methods, we refer to [3,4,9,10,12,22,24,26,32,35] and the references therein.…”

Section: Introductionmentioning

confidence: 99%