Multiplicity of normalized solutions for a class of nonlinear Schrödinger–Poisson–Slater equations

Luo, Tingjian

doi:10.1016/j.jmaa.2014.02.038

Cited by 29 publications

(30 citation statements)

References 26 publications

(45 reference statements)

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“…The nonlocal term causes some mathematical difficulties that make the study of (1.1) more interesting. As we shall see, (1.1) is also different from the Schrödinger-Poisson equation (see [6,19,28]), which is another problem exhibiting the competition between local and nonlocal terms. We point out that (1.1) arises from seeking the standing wave solutions to the following nonlinear Schrödinger equations with the gauge field:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Normalized solutions for the Chern–Simons–Schrödinger equation in R^2

Li¹,

Luo²

2017

Ann. Acad. Sci. Fenn. Math.

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Abstract. In this paper, we study the existence and multiplicity of solutions with a prescribed L 2 -norm for a class of nonlinear Chern-Simons-Schrödinger equations in RTo get such solutions we look for critical points of the energy functional, we prove a sufficient condition for the nonexistence of constrain critical points of I on S r (c) for certain c and get infinitely many minimizers of I on S r (8π). For the value p ∈ (4, +∞) considered, the functional I is unbounded from below on S r (c). By using the constrained minimization method on a suitable submanifold of S r (c), we prove that for certain c > 0, I has a critical point on S r (c). After that, we get an H 1 -bifurcation result of our problem. Moreover, by using a minimax procedure, we prove that there are infinitely many critical points of I restricted on S r (c) for any c ∈ 0,.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

“…[2,3,4,6,7,8,18,19,20,27,28,36]. In [18], Jeanjean considered the following semi-linear Schrödinger equation:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Normalized solutions for the Chern–Simons–Schrödinger equation in R^2

Li¹,

Luo²

2017

Ann. Acad. Sci. Fenn. Math.

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“…[1,2,[6][7][8]13,17,20,22,26]. In [7,8,13], for p in some ranges and c > 0, by using the concentration-compactness method of Lions [18,19], the authors obtained the minimizers oñ…”

Section: Introductionmentioning

confidence: 99%

“…When 10 3 < p < 6, in [20], by using the methods developed for nonlinear Schrödinger equation in [3,14], the author obtained there are infinitely many normalized solutions to the Schrödinger-Poisson-Slater system. Since our equation is similar to the Schrödinger-Poisson-Slater system in many parts, so we can use some ideas developed for it.…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 3, in the 2 < p < 4 case, we will use the Krasnoselski genus to constructs critical points; In the p > 4 case, as for the nonlinear Schrödinger equation in [3] and Schrödinger-Poisson-Slater system in [20], we will use linking type theorem in [3] and the auxiliary function approach in [14] to construct bounded Palais-Smale sequences of (1.12). The linking type theorem in [3], is a variant of the fountain theorem, for more on the linking type theorem, we refer the reader to [3,25].…”

Section: Introductionmentioning

confidence: 99%

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Multiple normalized solutions of Chern–Simons–Schrödinger system

Yuan

2015

Nonlinear Differ. Equ. Appl.

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In this paper, we consider the following equationfor p > 2 and λ > 0, which appeared in Byeon et al. (J Funct Anal 263(6):1575-1608, 2012) to find the standing wave solutions of the ChernSimons-Schrödinger system. By using the minimax theorem, we get the multiplicity results for the L 2 -normalized solutions to the equation, and thus there are multiple L 2 -normalized solutions of the Chern-SimonsSchrödinger system. Mathematics Subject Classification. 35Q55, 35A15, 35B30.

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Existence of normalized solutions for the coupled Hartree–Fock type system

Wang

2021

Mathematische Nachrichten

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Standing waves solutions for a coupled Hartree-Fock type nonlocal elliptic system are considered. This nonlocal type problem was considered in the basic quantum chemistry model of small number of electrons interacting with static nucleii which can be approximated by Hartree or Hartree-Fock minimization problems. First, we prove the existence of normalized solutions for different ranges of the positive (attractive case) coupling parameter for the stationary system. Then we extend the results to systems with an arbitrary number of components. Finally, the orbital stability of the corresponding solitary waves for the related nonlocal elliptic system is also considered.

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Multiplicity of normalized solutions for a class of nonlinear Schrödinger–Poisson–Slater equations

Cited by 29 publications

References 26 publications

Normalized solutions for the Chern–Simons–Schrödinger equation in R^2

Normalized solutions for the Chern–Simons–Schrödinger equation in R^2

Multiple normalized solutions of Chern–Simons–Schrödinger system

Existence of normalized solutions for the coupled Hartree–Fock type system

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