Inventi Impact: Engineering Mathematics

Inventi:eem/57845/23

A Nonexistence Result for Choquard-Type Hamiltonian System

In this article, we establish a nonexistence result of nontrivial non-negative solutions for the following Choquard-type Hamiltonian system by the Pohožaev identity { } { } ( ) ( ) 1 2 2 2 , in \ 0 , , in \ 0 , , 0, when , p p N q q N v v v u u I x x u u u v v I x x u x v x x μ α α μ β β − −    −Δ + =  ∗           −Δ + =  ∗         → →∞   , when N ≥ 3 , 1 2 0 < μ ,μ < N , 0 1 2 μ ≤α ≤ , 0 2 2 μ ≤ β ≤ , p, q > 1 , and 1 2 ( ) 2 2 2 2 N N N p q +μ − α +μ − β + ≤ − , where 1 i N i I x μ −μ = and ∗ denotes the convolution in N , i = 1, 2 .