Results 41 to 50 of about 669 (68)

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
core   +3 more sources

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
doaj   +1 more source

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
doaj   +1 more source

Existence results for nonhomogeneous Choquard equation involving p-biharmonic operator and critical growth

Demonstratio Mathematica
In this article, we are interested in the existence of nontrivial solutions for the following nonhomogeneous Choquard equation involving the pp-biharmonic operator: M∫Ω∣Δu∣pdxΔp2u−Δpu=λ(∣x∣−μ⁎∣u∣q)∣u∣q−2u+∣u∣p*−2u+f,inΩ,u=Δu=0,on∂Ω,\left\{\begin{array}{l}
Hai Quan, Zhang Jing
doaj   +1 more source

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
doaj   +1 more source

Existence and concentration behavior of positive solutions to Schrödinger-Poisson-Slater equations

Advances in Nonlinear Analysis, 2023
This article is directed to the study of the following Schrödinger-Poisson-Slater type equation: −ε2Δu+V(x)u+ε−α(Iα∗∣u∣2)u=λ∣u∣p−1uinRN,-{\varepsilon }^{2}\Delta u+V\left(x)u+{\varepsilon }^{-\alpha }\left({I}_{\alpha }\ast | u{| }^{2})u=\lambda | u{| }^{
Li Yiqing, Zhang Binlin, Han Xiumei
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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  

Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent

Advances in Nonlinear Analysis
In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type −Δu+u2∗1∣4πx∣u=μf(x)∣u∣p−2u+g(x)∣u∣4uinR3,-\Delta u+\left({u}^{2}\ast \frac{1}{| 4\pi x| }\right)u=\mu f\left(x){| u| }^{p-2 ...
Zheng Tian-Tian, Lei Chun-Yu, Liao Jia-Feng   +2 more
doaj   +1 more source