Results 11 to 20 of about 11,810,041 (377)
Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group
Advanced Nonlinear Studies, 2022 This article is devoted to the study of the combined effects of logarithmic and critical nonlinearities for the Kirchhoff-Poisson system −M∫Ω∣∇Hu∣2dξΔHu+μϕu=λ∣u∣q−2uln∣u∣2+∣u∣2uinΩ,−ΔHϕ=u2inΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-M\left(\mathop ...
Pucci Patrizia, Ye Yiwei
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Critical transitions and perturbation growth directions [PDF]
Physical Review E, 2017 Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical
Nahal Sharafi +5 more
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Fractional NLS equations with magnetic field, critical frequency and critical growth [PDF]
Manuscripta mathematica, 2016 The paper is devoted to the study of singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field.
Binlin Zhang, M. Squassina, Zhang Xia
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AIMS Mathematics, 2022 In this article, we deal with the following fractional $ p $-Kirchhoff type equation $ \begin{equation*} \begin{cases} M\left( \int_{\mathbb{R}^{N}}\int_{\mathbb{R}^{N}}\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\right)(-\Delta)_p^su=\frac{|u|^{p_\alpha ...
Zusheng Chen , Hongmin Suo, Jun Lei
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Concentrating Solutions for a Fractional Kirchhoff Equation with Critical Growth [PDF]
Nonlinear Fractional Schrödinger Equations in R^N, 2018 In this paper we consider the following class of fractional Kirchhoff equations with critical growth: \begin{equation*} \left\{ \begin{array}{ll} \left(\varepsilon^{2s}a+\varepsilon^{4s-3}b\int_{\mathbb{R}^{3}}|(-\Delta)^{\frac{s}{2}}u|^{2}dx\right ...
V. Ambrosio
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Electronic Research Archive, 2022 In this article, we study the following bi-nonlocal Kirchhoff-Schr$ \ddot{\mathrm{o}} $dinger-Poisson system with critical growth: $ \begin{equation*} \begin{cases} -\left( \int_{\Omega}|\nabla u|^2dx\right)^r\Delta u+\phi u = u^5+\lambda\left ...
Guaiqi Tian , Hongmin Suo , Yucheng An
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Semiclassical states for Choquard type equations with critical growth: critical frequency case [PDF]
Nonlinearity, 2017 In this paper we are interested in the existence of semiclassical states for the Choquard type equation −ε2Δu+V(x)u=∫RNG(u(y))|x−y|μdyg(u)inRN, where 0 < μ < N, N ⩾ 3, ɛ is a positive parameter and G is the primitive of g which is of critical growth due ...
Yanheng Ding, Fashun Gao, Minbo Yang
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W1,p versus C1: The nonsmooth case involving critical growth
Bulletin of Mathematical Sciences, 2020 In this paper, we study a class of generalized and not necessarily differentiable functionals of the form J(u) =∫ΩG(x,∇u)dx −∫Ωj1(x,u)dx −∫∂Ωj2(x,u)dσ with functions j1: Ω × ℝ → ℝ, j2: ∂Ω × ℝ → ℝ that are only locally Lipschitz in the second ...
Yunru Bai +3 more
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Electronic Research Archive, 2023 In this article, we investigate the Kirchhoff-Schrödinger-Poisson type systems on the Heisenberg group of the following form: $ \begin{equation*} \left\{ \begin{array}{lll} {-(a+b\int_{\Omega}|\nabla_{H} u|^{p}d\xi)\Delta_{H, p}u-\mu\phi |u|^{p-2}u} =
Shujie Bai +2 more
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Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent
Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper, we study the existence of ground state sign-changing solutions for the following fourth-order elliptic equations of Kirchhoff type with critical exponent. More precisely, we consider \begin{equation*} \begin{cases} \Delta^2u - \left(1 +
Sihua Liang, Binlin Zhang
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