Existence of the non‐radially symmetric ground state for p‐Laplacian equations involving Choquard type | Zendy

Lin Zhensheng | Zendy; Chen Jianqing | Zendy; Tang Xiuli | Zendy

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Existence of the non‐radially symmetric ground state for p‐Laplacian equations involving Choquard type

Author(s) -

Lin Zhensheng,

Chen Jianqing,

Tang Xiuli

Publication year - 2020

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.6366

Subject(s) - mathematics , ground state , type (biology) , laplace operator , nonlinear system , p laplacian , constraint (computer aided design) , mathematical analysis , identity (music) , term (time) , combinatorics , variational method , mathematical physics , pure mathematics , geometry , quantum mechanics , physics , boundary value problem , ecology , acoustics , biology

We consider some p‐Laplacian type equations with sum of nonlocal term and subcritical nonlinearities. We prove the existence of the ground states, which are positive. Because of including p =2, these results extend the results of Li, Ma and Zhang [Nonlinear Analysis: Real World Application 45(2019) 1‐25]. When p =2, N =3, by a variant variational identity and a constraint set, we can prove the existence of a non‐radially symmetric solution. Moreover, this solution u( x 1 , x 2 , x 3 ) is radially symmetric with respect to ( x 1 , x 2 ) and odd with respect to x 3 .

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