论文标题
加权choquard方程与加权非本地术语扰动
Weighted Choquard equation perturbed with weighted nonlocal term
论文作者
论文摘要
我们研究以下问题$$ - {\ rm div}（v（x）| \ nabla u |^{m-2} \ nabla u）+v（x）| u |^{m-2 {m-2} u = \ big（| x |^{ - θ}*\ frac {| u |^{b}} {| x |^|^α} \ big）\ frac {| u |^{b-2}} {| x |^|^|^α} u++ λ\ big（| x |^{ - γ}*\ frac {| u |^{c}}} {| x |^ββ} \ big）\ frac {| u |^{c-2}} {| x |^β} u \ quad \ mbox {in} \ r^{n}，$$其中$ b，c，α，β> 0 $，$θ，γ\ in（0，n）$，$ n \ geq 3 $，$ 2 \ leq m <\ leq m <\ f \ \ f \ \ \ in \ in \ in \ in \ r $。在这里，我们关注的是地面溶液的存在和最少的能量标志解决方案，这将通过分别在相关的Nehari歧管和Nehari Nodal集合上使用最小化技术来完成。
We investigate the following problem $$ -{\rm div}(v(x)|\nabla u|^{m-2}\nabla u)+V(x)|u|^{m-2}u= \Big(|x|^{-θ}*\frac{|u|^{b}}{|x|^α}\Big)\frac{|u|^{b-2}}{|x|^α}u+λ\Big(|x|^{-γ}*\frac{|u|^{c}}{|x|^β}\Big)\frac{|u|^{c-2}}{|x|^β}u \quad\mbox{ in }\R^{N}, $$ where $b, c, α, β>0$, $θ,γ\in (0,N)$, $N\geq 3$, $2\leq m< \infty$ and $λ\in \R$. Here, we are concerned with the existence of groundstate solutions and least energy sign-changing solutions and that will be done by using the minimization techniques on the associated Nehari manifold and the Nehari nodal set respectively.
