A discrete boundary value problem with parameters in Banach space

In the present note we are concerned with the question of the existence and uniqueness of solutions of two-point boundary value problem for nonlinear difference equations with parameters in Banach space.The proof of the above problem is based on the method of successive approximation and fixed-point method

The Henstock-Kurzweil-Pettis integrals and existence theorems for the Cauchy problem

summary:In this paper we prove an existence theorem for the Cauchy problem $$x^{\prime }(t) = f(t, x(t)), \quad x(0) = x_0, \quad t \in I_{\alpha } = [0, \alpha ]$$ using the Henstock-Kurzweil-Pettis integral and its properties. The requirements on the function $f$ are not too restrictive: scalar measurability and weak sequential continuity with respect to the second variable. Moreover, we suppose that the function $f$ satisfies some conditions expressed in terms of measures of weak noncompactness

A discrete boundary value problem in Banach spaces

In this paper we present existence theorems for the second order discrete boundary 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 the weak noncompactness

A discrete boundary value problem in Banach spaces

In this paper we present existence theorems for the second order discrete boundary 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 the weak noncompactness

A discrete boundary value problem with parameters in Banach space

In the present note we are concerned with the question of the existence and uniqueness of solutions of two-point boundary value problem for nonlinear difference equations with parameters in Banach space.The proof of the above problem is based on the method of successive approximation and fixed-point method

Nonlinear fractional differential equations in nonreflexive Banach spaces and fractional calculus

The aim of this paper is to correct some ambiguities and inaccuracies in Agarwal et al. (Commun. Nonlinear Sci. Numer. Simul. 20(1): 59-73, 2015; Adv. Differ. Equ. 2013: 302, 2013, doi:10.1186/1687-1847-2013-302) and to present new ideas and approaches for fractional calculus and fractional differential equations in nonreflexive Banach spaces

Existence theorem for multivalued hyperbolic equation

The article contains no abstrac