一类带凹凸项的椭圆型偏微分方程解的存在性  

Existence of Solutions for A Class of Elliptic Partial Differential Equations with Concave-convex Term

作　　者：郑文静 陈尚杰[1,2] 李麟[1,2] ZHENG Wen-jing;CHEN Shang-jie;LI Lin(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]重庆工商大学经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《西华师范大学学报（自然科学版）》2023年第5期473-480,共8页Journal of China West Normal University(Natural Sciences)

基　　金：重庆市教育委员会基金项目(KJQN20190081);重庆工商大学基金项目(CTBUZDPTTD201909)。

摘　　要：该文主要研究全空间上的一类带有凹凸项的椭圆型偏微分方程:-(a+b∫R^(3)K(x)▽u^(2)d x)div(K(x)▽u)=μK(x)g(x,u)+K(x)f(x,u),x∈3,其中K(x)=exp{x^(2)/4}为权函数,非线性项中的函数g,f为连续函数。在给定非线性项g,f一些恰当的条件下,利用山路定理讨论并证明了一类带有凹凸项的椭圆型偏微分方程无穷多解的存在性。This paper mainly talks about a class of elliptic partial differential equations with concave and convex terms on the whole space:-(a+b∫R^(3)K(x)▽u^(2)d x)div(K(x)▽u)=μK(x)g(x,u)+K(x)f(x,u),x∈3,where K(x)=exp{x^(2)/4}is the weight function and the function g,f in the nonlinear term is a continuous function.Under some appropriate conditions of the nonlinear term g,f,the existence of infinitely many solutions for a class of elliptic partial differential equations with concave and convex terms is discussed and proved by the mountain pass theorem.

关 键 词：山路定理 变分法 偏微分方程 凹凸项 无穷多解 

分 类 号：O129[理学—数学]