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A non-local evolution equation model of cell-cell adhesion in higher dimensional space. [PDF]

J Biol Dyn, 2013
Dyson J, Gourley SA, Webb GF.
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Existence and uniqueness of solution for a singular elliptic differential equation

Advances in Nonlinear Analysis
In this article, we are concerned about the existence, uniqueness, and nonexistence of the positive solution for: −Δu−12(x⋅∇u)=μh(x)uq−1+λu−up,x∈RN,u(x)→0,as∣x∣→+∞,\left\{\begin{array}{l}-\Delta u-\frac{1}{2}\left(x\cdot \nabla u)=\mu h\left(x){u}^{q-1}+\
Gu Shanshan, Yang Bianxia, Shao Wenrui
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Existence of solutions for a class of quasilinear Schrödinger equations with Choquard-type nonlinearity

Advances in Nonlinear Analysis
For the following quasilinear Choquard-type equation: −Δu−Δ(u2)u+V(x)u=(Iμ*∣u∣p)∣u∣p−2u,x∈RN,-\Delta u-\Delta \left({u}^{2})u+V\left(x)u=\left({I}_{\mu }* {| u| }^{p}){| u| }^{p-2}u,\hspace{1em}x\in {{\mathbb{R}}}^{N}, where N≥3 ...
Shen Zifei, Yang Ning
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Solutions to the coupled Schrödinger systems with steep potential well and critical exponent

Advanced Nonlinear Studies
In the present paper, we consider the coupled Schrödinger systems with critical exponent:−Δui+λVi(x)+aiui=∑j=1dβijuj3uiui in R3,ui∈H1(RN),i=1,2,…,d, $$\begin{cases}-{\Delta}{u}_{i}+\left(\lambda {V}_{i}\left(x\right)+{a}_{i}\right){u}_{i}=\sum _{j=1}^{d}
Lv Zongyan, Tang Zhongwei
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Monotonicity and symmetry of positive solutions to fractional p(x, ⋅)-Laplacian equation in bounded and unbounded domains

Demonstratio Mathematica
In this paper, we consider the following nonlinear elliptic equations involving the fractional p(x, ⋅)-Laplacian:(−Δ)p(x,⋅)su(x)=g(x,u(x),∇u(x)),x∈Ω,u(x)>0,x∈Ω,u(x)≡0,x∈RN\Ω, $$\begin{cases}{\left(-{\Delta}\right)}_{p\left(x,\cdot \right)}^{s}u\left(x ...
Wang Pengyan, Wang Zhihao
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Solvability of a mathematical model of dissociative adsorption and associative desorption type