Results 31 to 40 of about 86 (75)

Symmetric results of a Hénon-type elliptic system with coupled linear part

Open Mathematics, 2022
In this article, we study the elliptic system: −Δu+μ1u=∣x∣αu3+λv,x∈Ω−Δv+μ2v=∣x∣αv3+λu,x∈Ωu,v>0,x∈Ω,u=v=0,x∈∂Ω,\left\{\begin{array}{ll}-\Delta u+{\mu }_{1}u=| x\hspace{-0.25em}{| }^{\alpha }{u}^{3}+\lambda v,& x\in \Omega \\ -\Delta v+{\mu }_{2}v=| x ...
Lou Zhenluo, Li Huimin, Zhang Ping
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Existence and non-degeneracy of the normalized spike solutions to the fractional Schrödinger equations

Advances in Nonlinear Analysis
The present study investigates the existence and non-degeneracy of normalized solutions for the following fractional Schrödinger equation: (−Δ)su+V(x)u=aup+μu,x∈RN,u∈Hs(RN){\left(-\Delta )}^{s}u+V\left(x)u=a{u}^{p}+\mu u,\hspace{1.0em}x\in {{\mathbb{R}}}^
Guo Qing, Zhang Yuhang
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Supersolutions to nonautonomous Choquard equations in general domains

Advances in Nonlinear Analysis, 2023
We consider the nonlocal quasilinear elliptic problem: −Δmu(x)=H(x)((Iα*(Qf(u)))(x))βg(u(x))inΩ,-{\Delta }_{m}u\left(x)=H\left(x){(\left({I}_{\alpha }* \left(Qf\left(u)))\left(x))}^{\beta }g\left(u\left(x))\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0 ...
Aghajani Asadollah, Kinnunen Juha
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Limiting profile of positive solutions to heterogeneous elliptic BVPs with nonlinear flux decaying to negative infinity on a portion of the boundary

Open Mathematics
This paper ascertains the limiting profile of the positive solutions of heterogeneous logistic elliptic boundary value problems under nonlinear mixed boundary conditions.
Cano-Casanova Santiago
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Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions

Advances in Nonlinear Analysis
We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign ...
Díaz Jesús Ildefonso, Hernández Jesús   +1 more
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Positive solutions for a nonhomogeneous Schrödinger-Poisson system

Advances in Nonlinear Analysis, 2022
In this article, we consider the following Schrödinger-Poisson system: −Δu+u+k(x)ϕ(x)u=f(x)∣u∣p−1u+g(x),x∈R3,−Δϕ=k(x)u2,x∈R3,\left\{\begin{array}{ll}-\Delta u+u+k\left(x)\phi \left(x)u=f\left(x)| u{| }^{p-1}u+g\left(x),& x\in {{\mathbb{R}}}^{3 ...
Zhang Jing, Niu Rui, Han Xiumei
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Touchdown solutions in general MEMS models

Advances in Nonlinear Analysis, 2023
We study general problems modeling electrostatic microelectromechanical systems devices (Pλ )φ(r,−u′(r))=λ∫0rf(s)g(u(s))ds,r∈(0,1 ...
Clemente Rodrigo, Marcos do Ó João, da Silva Esteban, Shamarova Evelina   +3 more
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Multiple positive solutions to a p-Kirchhoff equation with logarithmic terms and concave terms

Open Mathematics
In this article, we focus on a class of pp-Kirchhoff-type equations that include logarithmic and concave terms. By applying the variational method, we establish the existence and multiplicity of positive solutions.
Liang Jin-Ping, Wang Ran-Ran, Wang Yue
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Ground State for a Coupled Elliptic System with Critical Growth

Advanced Nonlinear Studies, 2018
We study the following coupled elliptic system with critical nonlinearities:
Wu Huiling, Li Yongqing
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Ground states of Schrödinger systems with the Chern-Simons gauge fields

Advanced Nonlinear Studies, 2023
We are concerned with the following coupled nonlinear Schrödinger system: −Δu+u+∫∣x∣∞h(s)su2(s)ds+h2(∣x∣)∣x∣2u=∣u∣2p−2u+b∣v∣p∣u∣p−2u,x∈R2,−Δv+ωv+∫∣x∣∞g(s)sv2(s)ds+g2(∣x∣)∣x∣2v=∣v∣2p−2v+b∣u∣p∣v∣p−2v,x∈R2,\left\{\begin{array}{l}-\Delta u+u+\left(\underset{|
Jiang Yahui, Chen Taiyong, Zhang Jianjun, Squassina Marco, Almousa Nouf   +4 more
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