Nodal Solutions with a Prescribed Number of Nodes for Quasilinear Schrödinger Equations with a Cubic Term  

作　　者：Jing LAI Na LIU Tao WANG 

机构地区：[1]College of Mathematics and Computing Science,Hunan University of Science and Technology,Hunan 411201,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2024年第5期681-696,共16页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12001188);the Natural Science Foundation of Hunan Province(Grant No.2022JJ30235)。

摘　　要：This paper is concerned with the existence of nodal solutions for the following quasilinear Schrödinger equation with a cubic term■where N≥3,λ>0,the function V(|x|)is a radially symmetric and positive potential.By using the variational method and energy comparison method,for any given integer k≥1,the above equation admits a radial nodal solution U_(k,4)^(λ)having exactly k nodes via a limit approach.Furthermore,the energy of U_9k,4)^(λ)is monotonically increasing in k and for any sequence{λ_n},up to a subsequence,■converges strongly to some■asλ_(n)→+∞,which is a radial nodal solution with exactly k nodes of the classical Schrödinger equation■Our results extend the existing ones in the literature from the super-cubic case to the cubic case.

关 键 词：quasilinear Schrödinger equations nodal solutions limit approach variational method 

分 类 号：O175.29[理学—数学]