ON THE UNIQUE SOLVABILITY OF A NON‐LOCAL BOUNDARY VALUE PROBLEM FOR LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Solvability Conditions for a Nonlocal Boundary Value Problem for Linear Functional Differential Equations

The aim of the paper is to find efficient conditions for the unique solvability of the problem u′(t) = `(u)(t) + q(t), u(a) = h(u) + c, where ` : C([a, b];R) → L([a, b];R) and h : C([a, b];R) → R are linear bounded operators, q ∈ L([a, b];R), and c ∈ R.

On Unique Solvability of Boundary Value Problems for Systems of Linear Functional Differential Equations

Solvability and the Unique Solvability of a Periodic Type Boundary Value Problem for First Order Scalar Functional Differential Equations

Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem u′(t) = F (u)(t), u(a)− λu(b) = h(u) are established, where F : C([a, b];R) → L([a, b];R) is a continuous operator satisfying the Carathéodory condition, h : C([a, b];R) → R is a continuous functional, and λ ∈ R+. 2000 Mathematics Subject Classification: 34K10.

On boundary value problem for fractional differential equations

In this paper‎, ‎we study the existence of solutions for a‎ ‎ fractional boundary value problem‎. ‎By using critical point theory‎ ‎ and variational methods‎, ‎we give some new criteria to guarantee‎ ‎ that‎ ‎ the problems have at least one solution and infinitely many solutions.

Nonlocal Boundary Value Problem for Strongly Singular Higher-Order Linear Functional-Differential Equations

For strongly singular higher-order differential equations with deviating arguments, under nonlocal boundary conditions, Agarwal-Kiguradze type theorems are established, which guarantee the presence of the Fredholm property for the problems considered. We also provide easily verifiable conditions that guarantee the existence of a unique solution of the problem. 2000 Mathematics Subject Classific...