WebApr 25, 2024 · The result holds true for N < \dfrac { (p-a) (p+3) + 4b} {p-1} and is sharp in the case that w and f are Hardy–Hénon potentials. We also prove the full classification of solutions which are stable outside a compact set to Gelfand equation -\Delta _N u = e^u in \mathbb {R}^N. Download to read the full article text.WebApr 16, 2024 · Synthetic preservatives are widely utilized by the food industry to inhibit the microbial contamination and increase food safety and shelf life. The excessive utilization of synthetic preservatives can have a negative impact on human health and the environment. There is a great interest to find out natural substances as possible food-preservatives. …
Liouville Type Theorem for Stable Solutions to Weighted
WebJan 5, 2004 · The underlying idea of the technique is to assume an infinite series solution of the form u =∑ n=0∞un, then apply Laplace transformation to the differential equation. The nonlinear term is then decomposed in terms of Adomian polynomials and an iterative algorithm is constructed for the determination of the un′ s in a recursive manner.WebThe Gelfand family name was found in the USA, the UK, and Scotland between 1841 and 1920. The most Gelfand families were found in USA in 1920. In 1920 there were 38 …lauren henry cnp
REPRESENTATION OF THE GENERALIZED FUNCTIONS OF …
WebDec 22, 2016 · F or the perturb ed Gelfand’s equation on the unit ball in two dimen- sions, Y. Du and Y. Lou [4] proved that the curve of positive solutions is exactly S -shaped, for sufficiently small values ...WebMar 18, 2024 · The main result in this paper is given in the following theorem. Theorem 1.1. For \(N<10s\), there is no stable solution of ().. As mentioned above, the Gelfand equation admits a stable solution when \(N \ge 10\).Therefore, Theorem 1.1 is optimal in the limit \(s\uparrow 1\).. To prove Theorem 1.1, we do not use monotonicity formula as in …just the two of us eminem lyrics