Results 41 to 50 of about 694 (86)

Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity

Advances in Nonlinear Analysis, 2020
We are concerned with the following quasilinear elliptic ...
Fang Xiangdong, Zhang Jianjun
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Multiple solutions for critical Choquard-Kirchhoff type equations

Advances in Nonlinear Analysis, 2020
In this article, we investigate multiplicity results for Choquard-Kirchhoff type equations, with Hardy-Littlewood-Sobolev critical exponents,
Liang Sihua, Pucci Patrizia, Zhang Binlin   +2 more
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Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent [PDF]

, 2006
The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $u_t - \Delta u + |\nabla u|^q = 0$ in the whole space $R^N$ is investigated for the critical exponent $q = (N+2)/(N+1)$.
Gallay, Thierry, Laurençot, Philippe
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Ground state solutions of nonlinear Schrödinger equations involving the fractional p-Laplacian and potential wells

Open Mathematics, 2022
The purpose of this paper is to investigate the ground state solutions for the following nonlinear Schrödinger equations involving the fractional p-Laplacian (−Δ)psu(x)+λV(x)u(x)p−1=u(x)q−1,u(x)≥0,x∈RN,{\left(-\Delta )}_{p}^{s}u\left(x)+\lambda V\left(x ...
Chen Yongpeng, Niu Miaomiao
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Existence and Concentration of Solutions for Choquard Equations with Steep Potential Well and Doubly Critical Exponents

Advanced Nonlinear Studies, 2021
In this paper, we investigate the non-autonomous Choquard ...
Li Yong-Yong, Li Gui-Dong, Tang Chun-Lei
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Existence and Convergence of Solutions to Fractional Pure Critical Exponent Problems

Advanced Nonlinear Studies, 2021
We study existence and convergence properties of least-energy symmetric solutions (l.e.s.s.) to the pure critical exponent ...
Hernández-Santamaría Víctor, Saldaña Alberto   +1 more
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Existence and Asymptotic Behavior of Positive Solutions for a Class of Quasilinear Schrödinger Equations

Advanced Nonlinear Studies, 2018
In this paper, we study the quasilinear Schrödinger equation -Δ⁢u+V⁢(x)⁢u-γ2⁢(Δ⁢u2)⁢u=|u|p-2⁢u{-\Delta u+V(x)u-\frac{\gamma}{2}(\Delta u^{2})u=|u|^{p-2}u}, x∈ℝN{x\in\mathbb{R}^{N}}, where V⁢(x):ℝN→ℝ{V(x):\mathbb{R}^{N}\to\mathbb{R}} is a given potential,
Wang Youjun, Shen Yaotian
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Blow-Up Results for Higher-Order Evolution Differential Inequalities in Exterior Domains

Advanced Nonlinear Studies, 2019
We consider a higher-order evolution differential inequality in an exterior domain of ℝN{\mathbb{R}^{N}}, N≥3{N\geq 3}, with Dirichlet and Neumann boundary conditions.
Jleli Mohamed, Kirane Mokhtar, Samet Bessem   +2 more
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Ground states for a fractional scalar field problem with critical growth

, 2016
We prove the existence of a ground state solution for the following fractional scalar field equation $(-\Delta)^{s} u= g(u)$ in $\mathbb{R}^{N}$ where $s\in (0,1), N> 2s$,$ (-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R ...
Ambrosio, Vincenzo
core  

Multiplicity of positive solutions for a concave-convex fractional elliptic system with critical growth

Demonstratio Mathematica
In this paper, the following fractional elliptic system involving critical growth terms is considered(−Δ)su=αα+β|u|α−2u|v|β+λ|u|q−2u|x|γ, inΩ,(−Δ)sv=βα+β|u|α|v|β−2v+μ|v|q−2v|x|γ, inΩ,u=v=0, on∂Ω, $$\begin{cases}{\left(-{\Delta}\right)}^{s}u=\frac{\alpha }
Kang Qiao, Liao Jia-Feng
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