Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction
In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region principle) and prove the symmetry and nonexis...
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doaj-24bdcdec93cd462bb2053dca8596c1922021-10-03T07:42:25ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-08-0111138541610.1515/anona-2021-0202Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interactionWang Jun0Institute of Applied System Analysis, Jiangsu University, Zhenjiang, 212013, P.R. ChinaIn the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region principle) and prove the symmetry and nonexistence of positive solution of this nonlocal system. Second, we make complete classification of positive solutions of the system in the critical case when some parameters are equal. Finally, we prove the existence of multiple nontrivial solutions in the critical case according to the different parameters ranges by using variational methods. To accomplish our results we establish the maximum principle for the fractional nonlocal system.https://doi.org/10.1515/anona-2021-0202fractional laplaciansnonlinear fractional hartree systemvariational methods35j6135j2035q5549j40 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wang Jun |
spellingShingle |
Wang Jun Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction Advances in Nonlinear Analysis fractional laplacians nonlinear fractional hartree system variational methods 35j61 35j20 35q55 49j40 |
author_facet |
Wang Jun |
author_sort |
Wang Jun |
title |
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction |
title_short |
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction |
title_full |
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction |
title_fullStr |
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction |
title_full_unstemmed |
Qualitative analysis for the nonlinear fractional Hartree type system with nonlocal interaction |
title_sort |
qualitative analysis for the nonlinear fractional hartree type system with nonlocal interaction |
publisher |
De Gruyter |
series |
Advances in Nonlinear Analysis |
issn |
2191-9496 2191-950X |
publishDate |
2021-08-01 |
description |
In the present paperwe study the existence of nontrivial solutions of a class of static coupled nonlinear fractional Hartree type system. First, we use the direct moving plane methods to establish the maximum principle(Decay at infinity and Narrow region principle) and prove the symmetry and nonexistence of positive solution of this nonlocal system. Second, we make complete classification of positive solutions of the system in the critical case when some parameters are equal. Finally, we prove the existence of multiple nontrivial solutions in the critical case according to the different parameters ranges by using variational methods. To accomplish our results we establish the maximum principle for the fractional nonlocal system. |
topic |
fractional laplacians nonlinear fractional hartree system variational methods 35j61 35j20 35q55 49j40 |
url |
https://doi.org/10.1515/anona-2021-0202 |
work_keys_str_mv |
AT wangjun qualitativeanalysisforthenonlinearfractionalhartreetypesystemwithnonlocalinteraction |
_version_ |
1716846250026860544 |