Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential

Wang, Liping; Zhao, Chunyi

doi:10.3934/dcds.2017071

Cited by 11 publications

(3 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…with (α, γ) in (1.6). Later on, many works are realized for the two component systems, to name a few, we refer the readers to [1,2,5,6,13,14,15,17,24,23,25] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Infinitely many solutions with simultaneous synchronized and segregated components for nonlinear Schrödinger systems

Ye¹

2023

Preprint

View full text Add to dashboard Cite

In this paper, we consider the following nonlinear Schrödinger system in R 3 :where N ≥ 3, Pj are nonnegative radial potentials, µj > 0 and βij = βji are coupling constants. This type of systems have been widely studied in the last decade, many purely synchronized or segregated solutions are constructed, but few considerations for simultaneous synchronized and segregated positive solutions exist. Using Lyapunov-Schmidt reduction method, we construct new type of solutions with simultaneous synchronization and segregation. Comparing to known results in the literature, the novelties are threefold. We prove the existence of infinitely many non-radial positive and also sign-changing vector solutions, where some components are synchronized but segregated with other components; the energy level can be arbitrarily large; and our approach works for any N ≥ 3.

show abstract

“…with (α, γ) in (1.6). Later on, many works are realized for the two component systems, to name a few, we refer the readers to [1,2,5,6,13,14,15,17,24,23,25] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Infinitely many solutions with simultaneous synchronized and segregated components for nonlinear Schrödinger systems

Ye¹

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…See Theorem 1.1 and 1.2 in [9]. Wang et al [10] has improved the results of [9], allowing larger class of potentials. The second leading order in (1.3) with m > 0 has been included.…”

Section: Introductionmentioning

confidence: 99%

Infinitely many segregated vector solutions of Schrodinger system

Kwon¹,

Min-Gi²,

Lee³

2021

Preprint

View full text Add to dashboard Cite

We consider the following system of Schrödinger equationswhere λ, α 0 , α 1 > 0 are positive constants, β ∈ R is the coupling constant, and µ : R N → R is a potential function. Continuing the work of Lin and Peng[6], we present a solution of the type where one species has a peak at the origin and the other species has many peaks over a circle, but as seen in the above, coupling terms are nonlinear.

show abstract

“…Later on, many works are realized for the two or more components of systems. We refer the readers to [1,2,3,5,8,9,17,20,21,24,25,26,27,28] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

School Mathematics Textbooks in China

Wang¹

2015

East China Normal University Scientific Reports

View full text Add to dashboard Cite

Let µ and ν be two probability measures on R d , where µ(dx) = e −V (x) dx R d e −V (x) dx for some V ∈ C 1 (R d ). Explicit sufficient conditions on V and ν are presented such that µ * ν satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, if V (x) = λ|x| 2 for some λ > 0 and ν(e λθ|•| 2 ) < ∞ for some θ > 1, then µ * ν satisfies the log-Sobolev inequality. This improves and extends the recent results on the log-Sobolev inequality derived in [20] for convolutions of the Gaussian measure and compactly supported probability measures. On the other hand, it is well known that the log-Sobolev inequality for µ * ν implies ν(e ε|•| 2 ) < ∞ for some ε > 0. RésuméDes conditions explicites suffisantes sur V et ν sont présentées telles que µ * ν satisfait des inégalités de Sobolev logarithmique, de Poincaré et de super-Poincaré. En particulier, si V (x) = λ|x| 2 pour quelque λ > 0 et ν(e λθ|•| 2 ) < ∞ avec θ > 1, alors µ * ν satisfait l'inégalité de Sobolev logarithmique. Cela améliore et étend des résultats récents sur l'inégalité de Sobolev logarithmique obtenus dans [20] pour des convolutions de la mesure de Gauss et des mesures de probabilité à support compact. D'autre part, il est bien connu que l'inégalité de Sobolev logarithmique pour µ * ν implique ν(e ε|•| 2 ) < ∞ pour quelque ε > 0.

show abstract

Infinitely many solutions for nonlinear Schrödinger equations with slow decaying of potential

Cited by 11 publications

References 35 publications

Infinitely many solutions with simultaneous synchronized and segregated components for nonlinear Schrödinger systems

Infinitely many solutions with simultaneous synchronized and segregated components for nonlinear Schrödinger systems

Infinitely many segregated vector solutions of Schrodinger system

School Mathematics Textbooks in China

Contact Info

Product

Resources

About