一类带有对数非线性项的拟线性椭圆方程解的存在性及多重性  

Existence and multiplicity of solutions for a quasilinear elliptic equations with logarithmic nonlinearity

作　　者：刘晓莉 贾高[1] LIU Xiao-li;JIA Gao(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《高校应用数学学报（A辑）》2022年第3期253-267,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然基金(11171220)。

摘　　要：讨论一类带有对数非线性项的拟线性椭圆方程解的存在性和多重性问题.对主项系数A(x,t)提出合适的条件,利用山路引理证明该问题存在山路解,进一步利用对称山路定理证明该问题存在无穷多个非平凡解.This paper considers the existence and multiplicity of solutions of a class of quasilinear elliptic equations with logarithmic nonlinearity.Under some appropriate conditions for the principal coefficient A(x,t),the Mountain Pass Lemma to prove the existence of one nontrivial solution.Furthermore,the infinitely many nontrivial solutions of the problem are obtained by using the Symmetry Mountain Pass Theorem.

关 键 词：拟线性椭圆方程 (wCPS)c条件 山路引理 对称山路定理 

分 类 号：O175.25[理学—数学]