Existence of the non-radially symmetric ground state for p-Laplacian equations involving Choquard type |
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| Authors: | Zhensheng Lin Jianqing Chen Xiuli Tang |
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| Institution: | 1. College of Mathematics and Informatics, Fujian Normal University, Qishan Campus, Fuzhou, China;2. College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Qishan Campus, Fuzhou, China |
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| Abstract: | 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(x1, x2, x3) is radially symmetric with respect to (x1, x2) and odd with respect to x3. |
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| Keywords: | Choquard type ground state solution non-radially symmetric solution p-Laplacian Poho
žaev identity |
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