We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent...

This paper deals with the three-point boundary value problem for the nonlinear singularly perturbed second-order systems. Especially, we focus on an analysis of the solutions in the right endpoint of considered interval from an appearance of the boundary layer point of view. We use the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear systems considered here.

The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in ${\ell }_p$ space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo’s type fixed point theorem. The result is illustrated with help of an example.

The paper deals with the multivalued boundary value problem $x^{\text{'}}\in A(t,x)x+F(t,x)$ for a.a. $t\in [a,b]$, $Mx\left(a\right)+Nx\left(b\right)=0$, in a separable, reflexive Banach space $E$. The nonlinearity $F$ is weakly upper semicontinuous in $x$. We prove the existence of global solutions in the Sobolev space $W^{1,p}([a,b],E)$ with $1<p<\infty$ endowed with the weak topology. We consider the case of multiple solutions of the associated homogeneous linearized problem. An example completes the discussion.

We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.

We consider boundary value problems for semilinear evolution inclusions. We establish the existence of extremal solutions. Using that result, we show that the evolution inclusion has periodic extremal trajectories. These results are then applied to closed loop control systems. Finally, an example of a semilinear parabolic distributed parameter control system is worked out in detail.

In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order $r\in (0,1]$.

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.

In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.

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.

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.