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Two solutions for Dirichlet double phase problems with variable exponents

Advanced Nonlinear Studies
This paper is devoted to the study of a double phase problem with variable exponents and Dirichlet boundary condition. Based on an abstract critical point theorem, we establish existence results under very general assumptions on the nonlinear term, such ...
Amoroso Eleonora, Bonanno Gabriele, D’Aguì Giuseppina, Winkert Patrick   +3 more
doaj   +1 more source

Normalized solutions of Schrödinger equations involving Moser-Trudinger critical growth

Advances in Nonlinear Analysis
In this article, we are concerned with the nonlinear Schrödinger equation −Δu+λu=μ∣u∣p−2u+f(u),inR2,-\Delta u+\lambda u=\mu {| u| }^{p-2}u+f\left(u),\hspace{1em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{2}, having prescribed ...
Li Gui-Dong, Zhang Jianjun
doaj   +1 more source

Limit profiles and the existence of bound-states in exterior domains for fractional Choquard equations with critical exponent

Advances in Nonlinear Analysis
This article is devoted to studying the existence of positive solutions to the following fractional Choquard equation: (−Δ)su+u=∫Ω∣u(y)∣p∣x−y∣N−αdy∣u∣p−2u+ε∫Ω∣u(y)∣2α,s*∣x−y∣N−αdy∣u∣2α,s*−2u,inΩ,u=0,onRN\Ω,\left\{\begin{array}{ll}{\left(-\Delta )}^{s}u+u=
Ye Fumei, Yu Shubin, Tang Chun-Lei
doaj   +1 more source

Critical fractional Schrödinger-Poisson systems with lower perturbations: the existence and concentration behavior of ground state solutions

Advances in Nonlinear Analysis
In this article, we study the following fractional Schrödinger-Poisson system: ε2s(−Δ)su+V(x)u+ϕu=f(u)+∣u∣2s*−2u,inR3,ε2t(−Δ)tϕ=u2,inR3,\left\{\begin{array}{ll}{\varepsilon }^{2s}{\left(-\Delta )}^{s}u+V\left(x)u+\phi u=f\left(u)+{| u| }^{{2}_{s}^{* }-2 ...
Feng Shenghao, Chen Jianhua, Huang Xianjiu   +2 more
doaj   +1 more source

Cauchy problem for a non-Newtonian filtration equation with slowly decaying volumetric moisture content

Advances in Nonlinear Analysis
This article is concerned with the qualitative properties for the Cauchy problem of a non-Newtonian filtration equation with a reaction source term and volumetric moisture content.
Huo Wentao, Fang Zhong Bo
doaj   +1 more source

A variational approach to a singular elliptic system involving critical Sobolev-Hardy exponents and concave-convex nonlinearities

The Mathematical Scientist, 2013
N. Nyamoradi
semanticscholar   +2 more sources

Blow-up and global existence profile of a class of fully nonlinear degenerate parabolic equations

Open Mathematics, 2011
Li Jing, Yin Jingxue, Jin Chunhua
doaj   +1 more source

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Energy Estimate Related to a Hardy-Trudinger-Moser Inequality

Journal of Partial Differential Equations, 2019
Let B1 be a unit disc of R2, and H be a completion of C∞ 0 (B1) under the norm ∥u∥H = ∫ B1 ( |∇u|2− u 2 (1−|x|2)2 ) dx. Using blow-up analysis, Wang-Ye [1] proved existence of extremals for a Hardy-TrudingerMoser inequality.
Yunyan Yang sci
semanticscholar   +1 more source

Critical Exponents for the Heat Conduction Equation with a Nonlinear Boundary Condition

, 2013
We consider the heat conduction equation ut = ∇·(|∇u| m−1 ∇u )( m> 1),x∈ R N ,t >0, subject to the nonlinear boundary condition −|∇u| m−1 ∂u ∂x1 = u p ,x1 =0 ,t >0, in multi-dimension.
W. Du, Zhongping Li
semanticscholar   +1 more source

Decay of Solutions to a 2D Schrödinger Equation

, 2011
Let u∈C(R,H1) be the solution to the initial value problem for a 2D semilinear Schrodinger equation with exponential type nonlinearity, given in [1]. We prove that the Lr norms of u decay as t→±∞, provided that r>2.
Saanouni Tarek
semanticscholar   +1 more source