In this paper we obtain existence conditions and an explicit closed form expression of the general solution of twopoint boundary value problems for coupled systems of second order differential equations with a singularity of the first kind. The approach is algebraic and is based on a matrix representation of the system as a second order Euler matrix differential equation that avoids the increase of the problem dimension derived from the standard reduction of the order method.

We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.

This paper is concerned with the existence of solutions for some class of functional integrodifferential equations via Leray-Schauder Alternative. These equations arised in the study of second order boundary value problems for functional differential equations with nonlinear boundary conditions.

In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.

Let $f:[a,b]\times {ℝ}^{n+1}\to ℝ$ be a Carath’eodory’s function. Let $\left\{t_h\right\}$, with $t_h\in [a,b]$, and $\left\{x_h\right\}$ be two real sequences. In this paper, the family of boundary value problems $$\left\{\begin{array}{c}{x}^{\left(k\right)}=f\left(t,x,x^{\text{'}},...,x^{\left(n\right)}\right)x^{\left(i\right)}\left(t_i\right)=x_i,i=0,1,...,k-1\hfill \end{array}\right.(k=n+1,n+2,n+3,...)$$ is considered. It is proved that these boundary value problems admit at least a solution for each $k\ge \nu$, where $\nu \ge n+1$ is a suitable integer. Some particular cases, obtained by specializing the sequence $\left\{t_h\right\}$, are pointed out. Similar results are also proved for the Picard problem.

This paper surveys a number of recent results obtained by C. Bereanu and the author in existence results for second order differential equations of the form (ϕ(u'))' = f(t,u,u') submitted to various boundary conditions. In the equation, ϕ: ℝ → ≤ ]-a,a[ is a homeomorphism such that ϕ(0) = 0. An important motivation is the case of the curvature operator, where ϕ(s) = s/√(1+s²). The problems are reduced to fixed point problems in suitable function space, to which Leray-Schauder...

We use the method of quasilinearization to boundary value problems of ordinary differential equations showing that the corresponding monotone iterations converge to the unique solution of our problem and this convergence is quadratic.

In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.

In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation $-y^{\text{'}\text{'}}+qy=f$, where $q$ and $f$ are Henstock-Kurzweil integrable functions on $[a,b]$. Results presented in this article are generalizations of the classical results for the Lebesgue integral.