Results 1 to 10 of about 586 (91)

Stability and critical dimension for Kirchhoff systems in closed manifolds

Advanced Nonlinear Studies
The Kirchhoff equation was proposed in 1883 by Kirchhoff [Vorlesungen über Mechanik, Leipzig, Teubner, 1883] as an extension of the classical D’Alembert’s wave equation for the vibration of elastic strings. Almost one century later, Jacques Louis Lions [“
Hebey Emmanuel
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Ground states for fractional Kirchhoff double-phase problem with logarithmic nonlinearity

Demonstratio Mathematica
Our primary objective is to study the solvability of two kinds of fractional Kirchhoff double-phase problem involving logarithmic nonlinearity in RN{{\mathbb{R}}}^{N} via the variational approach.
Cheng Yu, Shang Suiming, Bai Zhanbing
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Multiple solutions for the quasilinear Choquard equation with Berestycki-Lions-type nonlinearities

Advances in Nonlinear Analysis
In this article, we study the following quasilinear equation with nonlocal nonlinearity −Δu−κuΔ(u2)+λu=(∣x∣−μ*F(u))f(u),inRN,-\Delta u-\kappa u\Delta \left({u}^{2})+\lambda u=\left({| x| }^{-\mu }* F\left(u))f\left(u),\hspace{1em}\hspace{0.1em}\text{in ...
Jia Yue, Yang Xianyong
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Standing-wave solutions to a system of non-linear Klein–Gordon equations with a small energy/charge ratio

Advances in Nonlinear Analysis, 2014
We prove the existence of standing-wave solutions to a system of non-linear Klein–Gordon equations on ℝN with N ≥ 3. Our solutions are characterised by a small energy/charge ratio, appropriately defined.
Garrisi Daniele
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On a logarithmic Hartree equation

Advances in Nonlinear Analysis, 2019
We study the existence of radially symmetric solutions for a nonlinear planar Schrödinger-Poisson system in presence of a superlinear reaction term which doesn’t satisfy the Ambrosetti-Rabinowitz condition. The system is re-written as a nonlinear Hartree
Bernini Federico, Mugnai Dimitri
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On multiplicity of solutions to nonlinear Dirac equation with local super-quadratic growth

Advances in Nonlinear Analysis
In this article, we study the following nonlinear Dirac equation: −iα⋅∇u+aβu+V(x)u=g(x,∣u∣)u,x∈R3.-i\alpha \hspace{0.33em}\cdot \hspace{0.33em}\nabla u+a\beta u+V\left(x)u=g\left(x,| u| )u,\hspace{1em}x\in {{\mathbb{R}}}^{3}.
Liao Fangfang, Chen Tiantian
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On coupled systems of nonlinear Schrödinger and Choquard equations with distinct exponents

Advanced Nonlinear Studies
In this paper, we are interested in the existence of a positive solution of the two coupled system of nonlinear Schrödinger and Choquard equations. Our equations admit the case that the nonlinearity exponents of two components are different.
Choi Dohoon, Lim Subong, Seok Jinmyoung
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Normalized solutions for the Kirchhoff equation with combined nonlinearities in ℝ4

Advances in Nonlinear Analysis
In this article, we study the following Kirchhoff equation with combined nonlinearities: −a+b∫R4∣∇u∣2dxΔu+λu=μ∣u∣q−2u+∣u∣2u,inR4,∫R4∣u∣2dx=c2,\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{4}}{| \nabla u| }^{2}{\rm ...
Qiu Xin, Ou Zeng-Qi, Tang Chun-Lei, Lv Ying   +3 more
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Normalized solutions for Sobolev critical fractional Schrödinger equation

Advances in Nonlinear Analysis
In the present study, we investigate the existence of the normalized solutions to Sobolev critical fractional Schrödinger equation: (−Δ)su+λu=f(u)+∣u∣2s*−2u,inRN,(Pm)∫RN∣u∣2dx=m2,\hspace{14em}\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+\lambda u=f ...
Li Quanqing, Nie Jianjun, Wang Wenbo, Zhou Jianwen   +3 more
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Interior regularity of obstacle problems for nonlinear subelliptic systems with VMO coefficients. [PDF]

J Inequal Appl, 2018
Du G, Li F.
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