Results 21 to 30 of about 60 (54)

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Positive solutions for the fractional Schrödinger equations with logarithmic and critical non‐linearities

Transactions of the London Mathematical Society, 2021
In this paper, we study a class of fractional Schrödinger equations involving logarithmic and critical non‐linearities on an unbounded domain, and show that such an equation with positive or sign‐changing weight potentials admits at least one positive ...
Haining Fan, Zhaosheng Feng, Xingjie Yan
doaj   +1 more source

Supercritical Hénon-type equation with a forcing term

Advances in Nonlinear Analysis
This article is concerned with the structure of solutions to the elliptic problem for a Hénon-type equation with a forcing term: −Δu=α(x)up+κμ,inRN,u>0,inRN,(Pκ)\hspace{11.3em}-\Delta u=\alpha \left(x){u}^{p}+\kappa \mu ,\hspace{1.0em}\hspace{0.1em}\text{
Ishige Kazuhiro, Katayama Sho
doaj   +1 more source

The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
doaj   +1 more source

Existence of Ground States of Fractional Schrödinger Equations

Advanced Nonlinear Studies, 2021
We consider ground states of the nonlinear fractional Schrödinger equation with ...
Ma Li, Li Zhenxiong
doaj   +1 more source

Ground state solutions and multiple positive solutions for nonhomogeneous Kirchhoff equation with Berestycki-Lions type conditions

Demonstratio Mathematica
This article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em ...
Huang Lanxin, Su Jiabao
doaj   +1 more source