一类梯度自然增长的拟线性椭圆型方程分布正解的存在性与多重性  

The Existence and Multiplicity of the Distributional Positive Solutions for a Class of Quasi-linear Elliptic Equations with Natural Growth in the Gradient

作　　者：胡业新 叶玉全 李枫柏 HU Yexin;YE Yuquan;LI Fengbai(School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]上海财经大学数学学院,上海200433

出　　处：《应用数学》2021年第4期800-806,共7页Mathematica Applicata

基　　金：国家自然科学基金(2015110605)。

摘　　要：本文研究一类梯度自然增长的拟线性椭圆型方程齐次边值问题在分布意义下正解的存在性与多重性.利用变分方法和扰动理论证明了相应的能量泛函在Banach空间W_(0)^(1,p)(Ω)中至少具有有限多个临界点,这推广了椭圆型方程弱解的多重性结果.In this paper, we study the existence and multiplicity of the distributional positive solutions for a class of homogeneous boundary value problem of quasi-linear elliptic equations with natural growth in the gradient. By using variational methods and the perturbation theory, we prove that the corresponding energy functional has at least finitely many critical points in Banach space W_(0)^(1,p)(Ω),which extends the multiplicity result of the weak solutions of quasi-linear elliptic equations.

关 键 词：梯度自然增长 扰动泛函 分布正解 临界点理论 

分 类 号：O175.25[理学—数学]