Nonlocal boundary value problems with BV-type data

Abstract

In this paper we present some existence and uniqueness results for solutions of second order boundary value problems, which are functions of bounded variation along with their derivatives. To this end, we apply fixed point theorems to an equivalent nonlinear perturbed Hammerstein integral equation. Here we consider non-standard boundary conditions like coupled boundary conditions, uncoupled boundary conditions, or integral-type boundary conditions. We also prove an abstract result concerning the spectral radii of some general classes of operators which applies to all boundary value problems mentioned above. The abstract results are throughout illustrated by a large number of examples.

Keywords

• boundary value problem
• bounded variation
• spectral radius