Results 41 to 50 of about 217 (68)
Some remarks about the summability of nonlocal nonlinear problems
Advances in Nonlinear Analysis, 2015 In this note, we will study the problem (-Δ)psu = f(x) on Ω, u = 0 in ℝN∖Ω, where 0 < s < 1, (-Δ)ps is the nonlocal p-Laplacian defined below, Ω is a smooth bounded domain. The main point studied in this work is to prove, adapting the techniques used in [
Barrios Begoña +2 more
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Ground-state solutions for fractional Kirchhoff-Choquard equations with critical growth
Advances in Nonlinear AnalysisWe study the following fractional Kirchhoff-Choquard equation: a+b∫RN(−Δ)s2u2dx(−Δ)su+V(x)u=(Iμ*F(u))f(u),x∈RN,u∈Hs(RN),\left\{\begin{array}{l}\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{\left|{\left(-\Delta )}^{\frac{s}{2}}u\right|}
Yang Jie, Chen Haibo
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Potential and monotone homeomorphisms in Banach spaces
Advances in Nonlinear AnalysisUsing the Ekeland variational principle and the mountain pass lemma we prove some properties about potential homeomorphisms between a real Banach space and its dual.
Bełdziński Michał, Galewski Marek
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Advanced Nonlinear StudiesIn this paper we study the following nonlinear fractional Hartree (or Choquard-Pekar) equation (−Δ)su+μu=(Iα*F(u))F′(u) inRN, ${\left(-{\Delta}\right)}^{s}u+\mu u=\left({I}_{\alpha }{\ast}F\left(u\right)\right){F}^{\prime }\left(u\right)\quad \text{in} {\
Cingolani Silvia +2 more
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Open MathematicsIn this article, we investigate the following Schrödinger equation: −Δu−μ∣x∣2u=g(u)inRN,-\Delta u-\frac{\mu }{{| x| }^{2}}u=g\left(u)\hspace{1em}{\rm{in}}\hspace{0.33em}{{\mathbb{R}}}^{N}, where N≥3N\ge 3, μ∣x∣2\frac{\mu }{{| x| }^{2}} is called the ...
Zhou Shan
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On multiplicity of solutions to nonlinear Dirac equation with local super-quadratic growth
Advances in Nonlinear AnalysisIn 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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Existence of three solutions for two quasilinear Laplacian systems on graphs
Demonstratio MathematicaWe deal with the existence of three distinct solutions for a poly-Laplacian system with a parameter on finite graphs and a (p,q)\left(p,q)-Laplacian system with a parameter on locally finite graphs. The main tool is an abstract critical point theorem in [
Pang Yan, Zhang Xingyong
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On the existence of solutions to adversarial training in multiclass classification
European Journal of Applied MathematicsAdversarial training is a min-max optimization problem that is designed to construct robust classifiers against adversarial perturbations of data. We study three models of adversarial training in the multiclass agnostic-classifier setting.
Nicolás García Trillos +2 more
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Ground state solutions for a class of nonlinear Maxwell-Dirac system [PDF]
, 2015 This paper is concerned with the following nonlinear Maxwell-Dirac system\begin{equation*}\begin{cases}\displaystyle-i\sum^{3}_{k=1}\alpha_{k}\partial_{k}u + a\beta u + \omega u-\phi u =F_{u}(x,u),\\-\Delta \phi=4\pi|u|^{2,\\\end{cases} \end{equation ...
Tang, Xianhua, Zhang, Jian, Zhang, Wen
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Minimal energy problems for strongly singular Riesz kernels [PDF]
, 2015 We study minimal energy problems for strongly singular Riesz kernels on a manifold. Based on the spatial energy of harmonic double layer potentials, we are motivated to formulate the natural regularization of such problems by switching to Hadamard's ...
Harbrecht, Helmut +2 more
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