Results 41 to 50 of about 458 (89)

Ground states of Schrödinger systems with the Chern-Simons gauge fields

Advanced Nonlinear Studies, 2023
We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui, Chen Taiyong, Zhang Jianjun, Squassina Marco, Almousa Nouf   +4 more
doaj   +1 more source

Supercritical Hénon-type equation with a forcing term

Advances in Nonlinear Analysis
This article is concerned with the structure of solutions to the elliptic problem for a Hénon-type equation with a forcing term: −Δu=α(x)up+κμ,inRN,u>0,inRN,(Pκ)\hspace{11.3em}-\Delta u=\alpha \left(x){u}^{p}+\kappa \mu ,\hspace{1.0em}\hspace{0.1em}\text{
Ishige Kazuhiro, Katayama Sho
doaj   +1 more source

Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities

Transactions of the London Mathematical Society, 2021
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
doaj   +1 more source

The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
doaj   +1 more source

Ground state solutions and multiple positive solutions for nonhomogeneous Kirchhoff equation with Berestycki-Lions type conditions

Demonstratio Mathematica
This article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em ...
Huang Lanxin, Su Jiabao
doaj   +1 more source

Existence of Ground States of Fractional Schrödinger Equations

Advanced Nonlinear Studies, 2021
We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
doaj   +1 more source

Torsion and ground state maxima: close but not the same

, 2015
Could the location of the maximum point for a positive solution of a semilinear Poisson equation on a convex domain be independent of the form of the nonlinearity? Cima and Derrick found certain evidence for this surprising conjecture.
Benson, Brian A., Laugesen, Richard S., Minion, Michael, Siudeja, Bartlomiej A.   +3 more
core  

Concentration phenomena for a fractional relativistic Schrödinger equation with critical growth

Advances in Nonlinear Analysis
In this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: (−Δ+m2)su+V(εx)u=f(u)+u2s*−1inRN,u∈Hs(RN),u>0inRN,\left\{\begin{array}{ll}{\left(-\Delta +{m}^{2})}^{s}u+V\left(\varepsilon x)u=f\left(u)
Ambrosio Vincenzo
doaj   +1 more source

A uniqueness result for the fractional Schrödinger-Poisson system with strong singularity

Open Mathematics
This article considers existence of solution for a class of fractional Schrödinger-Poisson system. By using the Nehari method and the variational method, we obtain a uniqueness result for positive solutions.
Wang Li, Chen Renhua, Zhong Qiaocheng, Wang Jun, Li Fang   +4 more
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On the solutions of a singular elliptic equation concentrating on a circle

Advances in Nonlinear Analysis, 2014
Let A={x∈ℝ2N+2 ...
Manna Bhakti B., Srikanth P. Chakravarthy   +1 more
doaj   +1 more source