一类含有一般非线性项的p-Laplacian方程的基态解  

Ground state solutions for a class of p-Laplacian equations with a general nonlinear term

作　　者：何毅 郑海东 HE Yi;ZHENG Haidong(College of Mathematics and Statistics,South-Central Minzu University,Wuhan 430074,China)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2024年第6期851-858,共8页Journal of South-Central Minzu University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11601530)。

摘　　要：研究了一类非线性p-Laplacian方程:-Δ_(p)u+|u|^(p-2)u=(I_(α)*F(u))f(u),x∈R^(N),其中p∈[2,+∞),N>p,α∈(0,N),F是f的原函数,I_(α)是Riesz位势.在一定的假设下,利用一般极小极大原理,构造了一个特殊的与Pohozaev恒等式相关的有界(PS)序列,证明了这一类p-Laplacian方程基态解的存在性.特别地,f所满足的条件被认为几乎是最优的.The following class of nonlinear p-Laplacian equation is considered::-Δ_(p)u+|u|^(p-2)u=(I_(α)*F(u))f(u),x∈R^(N),where p∈[2,+∞),N>p,α∈(0,N),F is the primitive function of f,Iαis the Riesz potential.Under certain assumptions,a special bounded(PS)sequence is constructed,which is related to the Pohozaev’s identity by the general minimax principle,and the existence of ground state solutions is proved for this class of p-Laplacian equations.In particular,the conditions on f is considered to be almost optimal.

关 键 词：P-LAPLACIAN方程 基态解 临界增长 

分 类 号：O175.29[理学—数学]