Existence of positive solutions for singular impulsive differential equations with integral boundary conditions on an infinite interval in Banach spaces

In this paper, the Mönch fixed point theorem is used to investigate the existence of positive solutions for the second-order boundary value problem with integral boundary conditions of nonlinear impulsive differential equations on an infinite interval in a Banach space

Multiple Positive Solutions of the Singular Boundary Value Problem for Second-Order Impulsive Differential Equations on the Half-Line

This paper uses a fixed point theorem in cones to investigate the multiple positive solutions of a boundary value problem for second-order impulsive singular differential equations on the half-line. The conditions for the existence of multiple positive solutions are established.This work is supported by the National Nature Science Foundation of P. R.China 10871063 and Scientific Research Fund of Hunan Provincial Education Department 07A038 , partially supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, project no.PGIDIT06PXIB207023PRS

Mixed Boundary Value Problem for Nonlinear Fractional Volterra Integral Equation

In this paper we present the existence of solutions for a nonlinear fractional integral equation of Volterra type with mixed boundary conditions, some necessary hypotheses have been developed to prove the existence of solutions to the proposed equation. Krasnoselskii Theorem, Banach Contraction principle, and Leray-Schauder degree theory are the basic theorems used here to find the results. A simple example of the application of the main result is presented

Fuzzy Solutions to Second Order Three Point Boundary Value Problem

In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum of the Hausdorff distance between level sets is obtained. Then to further establish the existence, fixed point theorem for absolute retracts is used by taking consideration that space of fuzzy sets can be embedded isometrically as a cone in Banach space. Finally, an example is provided to illustrate the result

The convergence analysis and error estimation for unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity

© 2018, The Author(s). In this paper, we focus on the convergence analysis and error estimation for the unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the problem is established. Then, from the developed iterative technique, the sequences converging uniformly to the unique solution are formulated, and the estimates of the error and the convergence rate are derived

The Ulam stability of non-linear Volterra integro-dynamic equations on time scales

This manuscript presents the Ulam stability results of non-linear Volterra integro-dynamic equation and its adjoint equation on time scales. First, we obtain the Ulam stability of adjoint equation by using the integrating factor method. Then, the Ulam stability of the corresponding equation is proved by means of the property of the exponential function and related results that are proved in adjoint equation with the help of integrating factor method. At the end, an example is given that shows the validity of our main results