带有对数非线性项的双相问题非平凡解的存在性  

Existence of nontrivial solutions for double phase problems with logarithmic nonlinearity

作　　者：熊明燕 储昌木 XIONG Mingyan;CHU Changmu(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵州贵阳550025

出　　处：《贵州科学》2024年第3期62-67,共6页Guizhou Science

基　　金：国家自然科学基金(No,11861021)。

摘　　要：研究了一类带有对数非线性项的双相问题的非平凡解。通常的双相问题的非线性项是多项式形式,但是本文所处理的非线性项是对数非线性项。通过计算可知此类带有对数非线性项双相问题的能量泛函满足山路型结构,再利用序列的有界性得到了Palais-Smale条件,最后结合山路引理,获得了该问题非平凡解的存在性结论。This paper studies the nontrivial solution of a class of double phase problem with logarithmic nonlinearity.The nonlinearity of the double phase problem is usually polynomial,but the nonlinearity in this paper is logarithmic nonlinearity.Through calculation,we can see that the energy functional of this kind of double phase problem with logarithmic nonlinearity satisfies the mountain geometry structure.The Palais-Smale condition is obtained through bounded sequence and the existence of the nontrivial solutions of the problem is obtained by mountain pass lemma.

关 键 词：双相问题 对数非线性项 山路引理 非平凡解 

分 类 号：O177.91[理学—数学]