Instability of Standing Waves for INLS with Inverse Square Potential

Saleh Almuthaybiri and Tarek Saanouni ()
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Saleh Almuthaybiri: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Tarek Saanouni: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2024, vol. 12, issue 19, 1-12

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.

Keywords: inhomogeneous Hartree equation; inverse square potential; nonlinear equations; instability; approximation; existence; uniqueness; ground states (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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