In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the...In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.展开更多
In this paper, we obtain some nonoscillatory theories of the functional differential equation (r(t)ψ(x(t))x (t)) + f(t, x(t), x(σ(t))) = 0, t ≥ t 0 , where r ∈ C 1 ([t 0 , ∞); (0, ∞)), ψ∈ C 1 (R, R) and f ∈ C...In this paper, we obtain some nonoscillatory theories of the functional differential equation (r(t)ψ(x(t))x (t)) + f(t, x(t), x(σ(t))) = 0, t ≥ t 0 , where r ∈ C 1 ([t 0 , ∞); (0, ∞)), ψ∈ C 1 (R, R) and f ∈ C([t 0 , ∞) × R × R, R).展开更多
In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible ...In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.展开更多
In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions usin...In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.展开更多
文摘In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.
基金Supported by the Key NSF of China(40333031)Supported by the NSF of Education Department of Hunan Province(04C646)
文摘In this paper, we obtain some nonoscillatory theories of the functional differential equation (r(t)ψ(x(t))x (t)) + f(t, x(t), x(σ(t))) = 0, t ≥ t 0 , where r ∈ C 1 ([t 0 , ∞); (0, ∞)), ψ∈ C 1 (R, R) and f ∈ C([t 0 , ∞) × R × R, R).
文摘In this paper, the authors consider the problem of existence of periodic solutions for a second order neutral functional differential system with nonlinear difference D-operator. For such a system, since the possible periodic solutions may not be differentiable, our method is based on topological degree theory of condensing field, not based on Leray Schauder topological degree theory associated to completely continuous field.
基金supported by University Grant Commission (UGC), India (No. G2/1287/UGC SAP DRS/2009)
文摘In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.
