Second order three boundary value problem in Banach spaces via Henstock and Henstock–Kurzweil–Pettis integral

Second-Order Boundary Value Problem with Integral Boundary Conditions

The unique solution of boundary value problems for nonlinear second-order integral-differential equations of mixed type in Banach spaces

In this paper, a class of two-point boundary value problems for nonlinear second-order integral–differential equations of mixed type is investigated in a real Banach space without making any compactness type assumption; we establish conditions for the existence of a unique solution of the equation and develop an iterative formula for approximation of the solution and a formula for estimating th...

A Discrete Boundary Value Problem in Banach Spaces

In this paper we present existence theorems for the second order discrete boundary value problem in Banach spaces under weaker conditions we have known. We suppose the weak sequential continuity and some conditions expressed in terms of the measure of weak noncompactness.

Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral boundary conditions in a Banach space. Moreover, an application is given to illustrate the main result.

Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces

and Applied Analysis 3 To prove our main results, for any h ∈ C J, E , we consider the Neumann boundary value problem NBVP of linear impulsive differential equation in E: −u′′ t Mu t h t , t ∈ J ′, −Δu′|t tk yk, k 1, 2, . . . , m, u′ 0 u′ 1 θ, 2.3 where M > 0, yk ∈ E, k 1, 2, . . . , m. Lemma 2.4. For any h ∈ C J, E , M > 0, and yk ∈ E, k 1, 2, . . . , m, the linear NBVP 2.3 has a unique soluti...