一类具有指数型增长的拟线性椭圆方程解的存在性与多重性  

Existenceand Multiplicity of Solutions for a Class of Quasilinear Elliptic Equations with Exponential Growth

作　　者：裴瑞昌[1] Rui Chang PEI(School of Mathematics and Statistics,Tianshui Normal University,Tianshui 741000,P.R.China)

机构地区：[1]天水师范学院数学与统计学院,天水741000

出　　处：《数学学报（中文版）》2022年第6期1045-1056,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11661070,12161077,11561059)。

摘　　要：本文研究一类具有次临界多项式增长或次临界指数型(临界指数型)增长的(p,2)-拉普拉斯方程一个正解及无穷多非平凡解的存在性,运用山路定理及喷泉定理,得到了拉普拉斯方程非平凡解的一些存在性结果.The main purpose of this paper is to investigate the existence of one positive solution and the existence of infinitely many nontrivial solutions for a class of(p,2)-Laplacian equation with subcritical polynomial growth and subcritical(critical)exponential growth.Some existence results for nontrivial solutions are established by using the mountain pass theorem and the fountain theorem.

关 键 词：(p 2)-拉普拉斯问题 次临界或临界指数型增长 山路定理 喷泉定理 

分 类 号：O175.5[理学—数学]