Bulletin of the Brazilian Mathematical Society, New Series ( IF 0.7 ) Pub Date : 2024-03-15 , DOI: 10.1007/s00574-024-00388-6 Romulo D. Carlos , Gustavo S. A. Costa , Giovany M. Figuereido
This paper is concerned with the existence and concentration of ground state solutions for the following class of elliptic Kirchhoff–Boussinesq type problems given by
$$\begin{aligned} \Delta ^{2} u \pm \Delta _{p} u +(1+\lambda V(x))u= f(u)\quad \text {in}\ {\mathbb {R}}^{4}, \end{aligned}$$where \(2< p< 4,\) \(f\in C( {\mathbb {R}}, {\mathbb {R}})\) is a nonlinearity which has subcritical or critical exponential growth at infinity and \(V\in C({\mathbb {R}}^4,{\mathbb {R}})\) is a potential that vanishes on a bounded domain \(\Omega \subset {\mathbb {R}}^4.\) Using variational methods, we show the existence of ground state solutions, which concentrates on a ground state solution of a Kirchhoff–Boussinesq type equation in \(\Omega .\)
中文翻译：
一类$${\mathbb {R}}^4$$指数增长的Kirchhoff-Boussinesq方程解的存在性和集中性
本文关注以下一类椭圆基尔霍夫-布辛涅斯克型问题的基态解的存在性和集中性：
$$\begin{对齐} \Delta ^{2} u \pm \Delta _{p} u +(1+\lambda V(x))u= f(u)\quad \text {in}\ {\ mathbb {R}}^{4}, \end{对齐}$$其中\(2< p< 4,\) \(f\in C( {\mathbb {R}}, {\mathbb {R}})\)是非线性，在无穷大处具有亚临界或临界指数增长，并且\ (V\in C({\mathbb {R}}^4,{\mathbb {R}})\)是在有界域\(\Omega \subset {\mathbb {R}}^4上消失的势.\)使用变分方法，我们证明了基态解的存在性，其中集中于\(\Omega .\)中的 Kirchhoff-Boussinesq 型方程的基态解
京公网安备 11010802027423号