Lyapunov inequalities for partial differential equations
نویسندگان
چکیده
منابع مشابه
Lyapunov inequalities for partial differential equations ✩
This paper is devoted to the study of Lp Lyapunov-type inequalities (1 p +∞) for linear partial differential equations. More precisely, we treat the case of Neumann boundary conditions on bounded and regular domains in RN . It is proved that the relation between the quantities p and N/2 plays a crucial role. This fact shows a deep difference with respect to the ordinary case. The linear study i...
متن کاملMatrix Lyapunov Inequalities for Ordinary and Elliptic Partial Differential Equations
This paper is devoted to the study of Lp Lyapunov-type inequalities for linear systems of equations with Neumann boundary conditions and for any constant p ≥ 1. We consider ordinary and elliptic problems. The results obtained in the linear case are combined with Schauder fixed point theorem to provide new results about the existence and uniqueness of solutions for resonant nonlinear problems. T...
متن کاملLyapunov-type Inequalities for Differential Equations
Let us consider the linear boundary value problem u′′(x) + a(x)u(x) = 0, x ∈ (0, L), u′(0) = u′(L) = 0, (0.1) where a ∈ Λ0 and Λ0 is defined by Λ0 = {a ∈ L∞(0, L) \ {0} : Z L 0 a(x) dx ≥ 0, (0.1) has nontrivial solutions}. Classical Lyapunov inequality states that Z L 0 a(x) dx > 4/L for any function a ∈ Λ0, where a(x) = max{a(x), 0}. The constant 4/L is optimal. Let us note that Lyapunov inequ...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Lyapunov-type integral inequalities for certain higher order differential equations
In this paper, we obtain Liapunov-type integral inequalities for certain nonlinear, nonhomogeneous differential equations of higher order with without any restriction on the zeros of their higher-order derivatives of the solutions by using elementary analysis. As an applications of our results, we show that oscillatory solutions of the equation converge to zero as t → ∞. Using these inequalitie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2006
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2005.12.011