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

On the right focal point boundary value problems for integro-differential equations

AbstractFor the nth order nonlinear integro-differential equations subject to right focal point boundary conditions we provide necessary and sufficient conditions for the existence, uniqueness, and convergence of an approximate iterative method

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

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

Higher order functional discontinuous boundary value problems on the half-line

In this paper, we consider a discontinuous, fully nonlinear, higher-order equation on the half-line, together with functional boundary conditions, given by general continuous functions with dependence on the several derivatives and asymptotic information on the (n−1)th derivative of the unknown function. These functional conditions generalize the usual boundary data and allow other types of global assumptions on the unknown function and its derivatives, such as nonlocal, integro-differential, infinite multipoint, with maximum or minimum arguments, among others. Considering the half-line as the domain carries on a lack of compactness, which is overcome with the definition of a space of weighted functions and norms, and the equiconvergence at ∞. In the last section, an example illustrates the applicability of our main result

Iterative solution to singular nth-order nonlocal boundary value problems

By using the cone theory and the Banach contraction mapping principle, we study the existence and uniqueness of an iterative solution to the singular nth-order nonlocal boundary value problems