Year: 2019
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 288–311
Abstract
For the Schrödinger system
{−Δuj+λjuj=k∑i=1βiju2iujin RN,uj(x)→0 as |x|→∞,j=1,⋯,k,
where k≥2 and N=2,3, we prove that for any λj>0 and βjj>0 and any positive integers pj, j=1,2,⋯,k, there exists b>0 such that if βij=βji≤b for all i≠j then there exists a radial solution (u1,u2,⋯,uk) with uj having exactly pj−1 zeros. Moreover, there exists a positive constant C0 such that if βij=βji≤b (i≠j) then any solution obtained satisfies
k∑i,j=1|βij|∫RNu2iu2j≤C0.
Therefore, the solutions exhibit a trend of phase separations as βij→−∞ for i≠j.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0009
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 3 : pp. 288–311
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Vector solution prescribed component-wise nodes Schrödinger system variational methods.
-
The number of positive solutions for nn‐coupled elliptic systems
Jing, Yongtao | Liu, Haidong | Liu, Yanyan | Liu, Zhaoli | Wei, JunchengJournal of the London Mathematical Society, Vol. 110 (2024), Iss. 6
https://doi.org/10.1112/jlms.70040 [Citations: 0] -
Ground state solutions for planar coupled system involving nonlinear Schrödinger equations with critical exponential growth
Wei, Jiuyang | Lin, Xiaoyan | Tang, XianhuaMathematical Methods in the Applied Sciences, Vol. 44 (2021), Iss. 11 P.9062
https://doi.org/10.1002/mma.7335 [Citations: 4] -
A coupled Schrödinger system with critical exponent
Liu, Haidong | Liu, ZhaoliCalculus of Variations and Partial Differential Equations, Vol. 59 (2020), Iss. 5
https://doi.org/10.1007/s00526-020-01803-8 [Citations: 13] -
Infinitely many nodal solutions of Kirchhoff-type equations with asymptotically cubic nonlinearity without oddness hypothesis
Li, Fuyi | Zhang, Cui | Liang, ZhanpingCalculus of Variations and Partial Differential Equations, Vol. 63 (2024), Iss. 7
https://doi.org/10.1007/s00526-024-02805-6 [Citations: 0] -
Infinitely many nodal solutions for a class of quasilinear elliptic equations
Yang, Xiaolong
Electronic Journal of Qualitative Theory of Differential Equations, Vol. (2021), Iss. 32 P.1
https://doi.org/10.14232/ejqtde.2021.1.32 [Citations: 0] -
Infinitely Many Nodal Solutions for Kirchhoff-Type Equations with Non-odd Nonlinearity
Li, Fuyi | Zhang, Cui | Liang, ZhanpingQualitative Theory of Dynamical Systems, Vol. 23 (2024), Iss. 1
https://doi.org/10.1007/s12346-023-00857-1 [Citations: 0] -
Nontrivial solutions for an elliptic system of Hamiltonian type
Zhi, Yanyan | Liu, XiaochunApplicable Analysis, Vol. 101 (2022), Iss. 14 P.5017
https://doi.org/10.1080/00036811.2021.1877684 [Citations: 0]