论文标题
具有竞争非本地术语的非线性标量场方程
Nonlinear scalar field equation with competing nonlocal terms
论文作者
论文摘要
我们找到了以下非局部问题$$-ΔU +ωU= \ big（i_α\ ast f（u）f（u）\ big）f（u） - \ big（i_β\ ast g（u）g（u）g（u）g（big）g（big）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）g（u）强加于$ f $和$ g $，其中$ n \ geq 3 $，$ 0 \ leqβ\ leq leq leqα<n $，$ω\ geq 0 $，$ f，g：\ mathbb {r} \ to \ mathbb {r} $连续功能与相应的primitive primitive $ f，g $ f，g $，$ i________________________________如果$β> 0 $，那么我们处理两个竞争的非本地术语，建模有吸引力和排斥性相互作用的电位。
We find radial and nonradial solutions to the following nonlocal problem $$-Δu +ωu= \big(I_α\ast F(u)\big)f(u)-\big(I_β\ast G(u)\big)g(u) \text{ in } \mathbb{R}^N$$ under general assumptions, in the spirit of Berestycki and Lions, imposed on $f$ and $g$, where $N\geq 3$, $0\leq β\leq α<N$, $ω\geq 0$, $f,g:\mathbb{R}\to \mathbb{R}$ are continuous functions with corresponding primitives $F,G$, and $I_α,I_β$ are the Riesz potentials. If $β>0$, then we deal with two competing nonlocal terms modelling attractive and repulsive interaction potentials.
