Year: 2024
Type: article
Abstract: This work studies an inhomogeneous generalized Hartree equation with inverse square potential. The purpose is to prove the existence and strong instability of inter-critical standing waves. This means that there are infinitely many data near to the ground state, such that the associated solution blows-up in finite time. The proof combines a variational analysis with the standard variance identity. The challenge is to deal with three difficulties: the singular potential |x|−2, an inhomogeneous term |x|−λ, and a non-local source term.
Source: Mathematics
DOI: 10.3390/math12192999
Authors: Saleh Almuthaybiri, Tarek Saanouni
Institution: Qassim University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
Funder: Qassim University
Awards: G1271011243, G5120360896
OpenAlex ID: W4402862154