Results 11 to 20 of about 11,751,266 (377)
In this article, we study the existence of multiple solutions to a generalized p(⋅)p\left(\cdot )-Laplace equation with two parameters involving critical growth.
Ho Ky, Sim Inbo
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Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group
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]
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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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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Fractional NLS equations with magnetic field, critical frequency and critical growth [PDF]
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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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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W1,p versus C1: The nonsmooth case involving critical growth
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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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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Concentrating Solutions for a Fractional Kirchhoff Equation with Critical Growth [PDF]
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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Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent
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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