一类拟线性椭圆型方程非平凡解的存在性  

Existence of Nontrivial Solutions for One Class of Quasilinear Elliptic Equations

作　　者：李鹏菲 樊自安 谢君辉 LI Pengfei;FAN Zi’an;XIE Junhui(College of Science,Hubei Minzu University,Enshi 445000,China;School of Mathematics and Statistics,Hubei Engineering University,Xiaogan 432000,China)

机构地区：[1]湖北民族大学理学院,湖北恩施445000 [2]湖北工程学院数学与统计学院,湖北孝感432000

出　　处：《湖北民族大学学报（自然科学版）》2020年第1期72-77,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：国家自然科学基金项目(11761030);湖北省自然科学基金项目(2017CFB352).

摘　　要：研究一类带边值问题的拟线性椭圆偏微分方程解的存在性,是微分方程理论研究的核心,也是这一领域的研究热点.利用变分方法、临界点理论等工具研究这类拟线性椭圆偏微分方程解的存在性具有深刻的物理和力学背景.本文主要应用山路引理以及变分原理,证明了一类带Dirichlet边界条件的拟线性椭圆型偏微分方程非平凡弱解的存在性.To study existence of solutions for quasilinear differential equations with boundary condition is the core of the theroetical of research and it is also one of the hot lopics in this field.It has a profound background on physics and mechanics to study existence of solutions for quasilinear differential equations with variational principle and critical point theory.In this paper,using Mountain Pass theorem and variational principle,we study the existence of nontrivial solutions for one class of quasilinear elliptic equations with Dirichlet boundary condition.

关 键 词：拟线性 椭圆方程 非平凡解 存在性 山路引理 

分 类 号：O175.25[理学—数学]