文献类型：期刊文献

英文题名：Normalized Solutions to a Class of (2, q)-Laplacian Equations in the Strongly Sublinear Regime

作者：Ding, Rui[1];Ji, Chao[1];Pucci, Patrizia[2]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Univ Perugia, Dipartimento Matemat & Informat, I-06123 Perugia, Italy

年份：2025

卷号：35

期号：3

外文期刊名：JOURNAL OF GEOMETRIC ANALYSIS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001423537100005)】；

基金：The authors would like to thank the anonymous referee for several valuable suggestions and comments which helped to improve the paper. C. Ji was partially supported by National Natural Science Foundation of China (No. 12171152). P. Pucci is a member of the Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni (GNAMPA) of the Instituto Nazionale di Alta Matematica (INdAM) and this paper was written under the auspices of GNAMPA-INdAM

语种：英文

外文关键词：(2, q)-Laplacian; Strongly sublinear; Least energy solutions; Multiple solutions; Variational methods

摘要：In this paper, we consider the existence and multiplicity of normalized solutions for the following (2, q)-Laplacian equation. integral-Delta u rho alpha + lambda alpha = g(u), x is an element of R-N, integral udx=c(2).
(6)
where 14 N. A div (IVu/-2Vu) is the 4-Laplacian operator, A is a Lagrange multiplier and e O is a constant. The nonlinearityg: R Ris con-tinuous and the behaviour of g at the origin is allowed to be strongly sublinear, i.e., lim g(x)/s-00, which includes the logarithmic nonlinearity
g(s) = slog s(2) (0.2)
We consider a family of approximating problems that can be set in H (RN) n D. (RN) and the corresponding least-energy solutions. Then, we prove that such a family of solutions converges to a least-energy solution to the original problem. Additionally, under certain assumptions about g that allow us to work in a suitable subspace of H-1 (R-N) D-1,D-q (R-N), we prove the existence of infinitely many solutions of the above (2, 4)-Laplacian equation.