On solutions of non-autonomous ordinary differential equations

2015

Annali di Matematica

Section: Introductionmentioning

confidence: 99%

On the behavior of Kneser solutions of nonlinear ordinary differential equations

2015

Annali di Matematica

“…The questions treated in this paper were studied earlier by a number of authors (see [1][2][3][4][5][7][8][9]). The questions treated in this paper were studied earlier by a number of authors (see [1][2][3][4][5][7][8][9]).…”

Section: Introductionmentioning

confidence: 99%

“…f (x)g(u)ϕ dx dt for any non-negative function ϕ ∈ C ∞ 0 (R n × (0, ∞)). The questions treated in this paper were studied earlier by a number of authors (see [1][2][3][4][5][7][8][9]). Our aim is to obtain conditions guaranteeing that every solution of equation (11) tends to 0 as t → ∞.…”

Section: Introductionmentioning

confidence: 99%

On the asymptotic behaviour of solutions of nonlinear parabolic equations

Proceedings of the Royal Society of Edinburgh: Section A Mathem

2006

“…(see[19, Lemma 2.3]). Let ψ : (0, ∞) → (0, ∞) and γ : (0, ∞) → (0, ∞) be measurable functions satisfying the conditionγ(ζ) ≤ ess inf (ζ/θ,θζ)…”

mentioning

confidence: 99%

On stabilization of solutions of higher order evolution inequalities

Shishkov

2019

Asymptotic Analysis

We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality |α|=m ∂ α a α (x, t, u) − u t ≥ f (x, t)g(u) in R n+1 + = R n × (0, ∞), m, n ≥ 1, stabilizes to zero as t → ∞. These conditions generalize the well-known Keller-Osserman condition on the grows of the function g at infinity.1991 Mathematics Subject Classification. 35K25, 35K55, 35K65, 35B09, 35B40. Key words and phrases. Higher order evolution inequalities; Nonlinearity; Stabilization. The work of the second author is supported by RUDN University, Project 5-100., then due to monotonicity of the function G we haveCombining the last two inequalities, we getwhence we again derive (3.20). In a similar way, it can be shown thatfor all i ∈ Ξ 2 . Really, taking into account (3.19), we haveIn view of the inequalitythis obviously implies (3.21). Further, summing (3.20) over all i ∈ Ξ 1 , we obtain ∞ J R (r 0 ,τ ) G −1/m (ζ/2)ζ 1/m−1 dζ + ∞ J R (r 0 ,τ ) dζ G(ζ/2)