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

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.