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This paper is concerned { ut = ∆u− χ1∇·(u∇v) + µ1u(1−u−a1w) in Ω×(0,∞), 0 = ∆v−v+w in Ω×(0,∞), wt = ∆w− χ2∇·(w∇z) + µ2w(1−a2u−w) in Ω×(0,∞), 0 = ∆z−z+u in Ω×(0,∞), with stabilization in the two-species–two chemicals chemotaxis-competition system where Ω is a bounded domain in R n (n ≥ 2) with smooth boundary, X1,X2 and µ1,µ2 are constants satisfying some conditions. About this system Tu–Mu–Zheng–Lin (Discrete Contin. Dyn. Syst.;2018;38;3617– 3636) showed global existence and stabilization of solutions under some smallness conditions for χ1 and χ2. Here energy arguments for seeing stabilization in the previous work were based on ideas in Bai–Winkler (Indiana Univ. Math. J.;2016;65;553–583); however, these ideas were recently improved by the first author (Discrete Contin. Dyn. Syst. Ser. S;2020;13;269–278), which implies that the result about stabilization in the previous work seems not to be the best. This paper gives an improvement of conditions for stabilization in the previous work. The feature of the proof is to use the Sylvester criterion in deriving energy estimates. [ABSTRACT FROM AUTHOR]

Background: Morphine is effective in palliative care for patients with end-stage heart failure; however, its use is avoided in patients with impaired renal function because it tends to induce adverse effects. Although oxycodone has been reported to be a useful alternative, the evidence is insufficient. Therefore, we investigated the safety and efficacy of oxycodone in eight patients with end-stage heart failure complicated by chronic kidney disease.  METHODS: This single-center retrospective study reviewed patients with end-stage heart failure who were referred to the heart failure multidisciplinary team at our institution and administered oxycodone for refractory dyspnea during hospitalization between January 2011 and December 2018. We examined the details of oxycodone usage, vital signs, and the Modified Borg Scale (MBS), which quantifies the symptoms of dyspnea and adverse events., Results: Oxycodone was administered for refractory dyspnea in eight patients with end-stage heart failure [mean age: 81 years, men: 4, New York Heart Association functional class IV: 8, median left ventricular ejection fraction: < 40% (n = 6) and ≥ 50% (n = 2)]. Renal function was reduced in all patients; the estimated glomerular filtration rate (eGFR) in seven patients was < 30 mL/min/1.73 m 2 . The median initial intravenous dose of oxycodone was 7.05 mg/day (range: 5-10 mg/day), and the average duration of administration was 15.8 days. Significant decreases in MBS (before: median 9, range 7-10 vs. after: median 2.5, range 1-8; p < 0.01) were observed at a median of 2.0 days (range: 2 h to 7 days) after beginning oxycodone administration. Systolic blood pressure, heart rate, and respiratory rate were not significantly altered after treatment. Adverse events, including constipation, nausea, and tremors, were observed in three patients. However, no lethal adverse events related to oxycodone treatment occurred during treatment., Conclusions: This study revealed the clinical practice of oxycodone treatment and suggested that it is an alternative therapy as a viable palliative for refractory dyspnea in patients with end-stage heart failure who should avoid the use of morphine., (© 2024. The Author(s).)