论文标题
一般Kirchhoff类型方程的存在和浓度结果
Existence and Concentration Results for the General Kirchhoff Type Equations
论文作者
论文摘要
我们考虑以下单一扰动的Kirchhoff类型方程$$ - \ varepsilon^2 m \ left（\ varepsilon^{2-n} {2-n} \ int \ int _ {\ r^n} | \ nabla u |^nabla u |^2 dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx d d d d dx dx dx） u \ in H^1（\ r^n），n \ geq 1，$$，其中$ m \在c（[0，\ infty））$ and $ v \ in C（\ r^n）$ in c（\ r^n）$均给出函数。在$ m $上的非常温和的假设下，我们证明了上述问题的单峰或多峰解决方案$ u_ \ varepsilon $，以直接的相应参数集中在拓扑稳定的$ V $的关键点上。这给了Figueiredo等人提出的一个开放问题提供了肯定的答案。 2014年[ARMA，213]。
We consider the following singularly perturbed Kirchhoff type equations $$-\varepsilon^2 M\left(\varepsilon^{2-N}\int_{\R^N}|\nabla u|^2 dx\right)Δu +V(x)u=|u|^{p-2}u~\hbox{in}~\R^N, u\in H^1(\R^N),N\geq 1,$$ where $M\in C([0,\infty))$ and $V\in C(\R^N)$ are given functions. Under very mild assumptions on $M$, we prove the existence of single-peak or multi-peak solution $u_\varepsilon$ for above problem, concentrating around topologically stable critical points of $V$, by a direct corresponding argument. This gives an affirmative answer to an open problem raised by Figueiredo et al. in 2014 [ARMA,213].
