We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
A new triple fixed-point theorem is applied to investigate the existence of at least triple positive solutions of fourth-order four-point boundary value problems for p-Laplacian dynamic equations on a time scale. The interesting point is that we choose an inversion technique employed by Avery and Peterson in 1998. Copyright q 2008 Mei-Qiang Feng et al. This… (More)
In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions with variable times involving the Caputo fractional derivative.
We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions depending on an eigenvalue parameter. Discussing the point spectrum and using the uniqueness theorem of analytic functions, we present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral… (More)
In this paper, a class of impulsive functional differential systems is investigated. It is proved that for the asymptotic stability of the zero solution of the system considered, it is sufficient that only some components of the right-hand side of the system are bounded for unbounded values of time. For functional differential equations without impulses,… (More)
This paper investigates parametric stability for nonlinear differential equations with " maxima ". Several sufficient conditions for parametric stability as well as uniform parametric stability are obtained based on the Razumikhin method. Two different types of Lyapunov functions have been applied. A comparison with scalar ordinary differential equations is… (More)
We establish a general form of sum-difference inequality in two variables, which includes both more than two distinct nonlinear sums without an assumption of monotonicity and a nonconstant term outside the sums. We employ a technique of monotonization and use a property of stronger monotonicity to give an estimate for the unknown function. Our result… (More)
The differential equation u (t) + Au(t) = f (t) (−∞ < t < ∞) in a general Banach space E with the strongly positive operator A is ill-posed in the Banach space C(E) = C(R,E) with norm ϕ C(E) = sup −∞<t<∞ ϕ(t) E. In the present paper, the well-posedness of this equation in the Hölder space C α (E) = C α (R,E) with norm ϕ C α (E) = sup −∞<t<∞ ϕ(t) E + sup… (More)
Let (u n) be a sequence of real numbers and let L be any (C,1) regular limitable method. We prove that, under some assumptions, if a sequence (u n) or its generator sequence (V (0) n (Δu)) generated regularly by a sequence in a class Ꮽ of sequences is a subsequential convergence condition for L, then for any integer m ≥ 1, the mth repeated arithmetic means… (More)