论文标题
一类具有广义标志潜力的Kirchhoff-Choquard方程的存在和多重性结果
Existence and multiplicity results for a class of Kirchhoff-Choquard equations with a generalized sign-changing potential
论文作者
论文摘要
在目前的工作中，我们关注以下Kirchhoff-choquard-type方程$$ -M（|| \ nabla u || _ {2}^{2}^{2}）ΔU + q（x） $ M：\ MATHBB {r} \ rightArrow \ Mathbb {r} $由$ m（t）= a+bt $，$μ> 0 $，$ v $，签名换去的潜力和可能的无界潜力，$ q $ a连续的外部电位和非线性$ f $具有指定性的重要增长。我们证明了在非平衡案例中的存在和多样性，并保证在退化情况下存在解决方案。
In the present work we are concerned with the following Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})Δu +Q(x)u + μ(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M: \mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ μ>0 $, $ V $ a sign-changing and possible unbounded potential, $ Q $ a continuous external potential and a nonlinearity $f$ with exponential critical growth. We prove existence and multiplicity of solutions in the nondegenerate case and guarantee the existence of solutions in the degenerate case.
