On the Solvability of Boundary Value Problems for an Abstract Bessel-Struve Equation

Abstract

We consider the Dirichlet and Neumann boundary value problems for the hyperbolic Bessel-Struve equation u″(t) + kt⁻¹(u′(t) - u′(0)) = Au(t) on the half-line t > 0, where k > 0 is a parameter and A is a densely defined closed linear operator in a complex Banach space E. Generally speaking, these problems are ill posed. We establish sufficient conditions on the operator coefficient A and the boundary elements for these problems to be uniquely solvable.