Galerkin boundary element methods for the solution of novel first kind Steklov–Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are investigated to solve potential type problems in twoand three-dimensional Lipschitz domains with nonlinear boundary conditions. For the numerical solution of the resulting Newton iterate linear boundary integral equations...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Johannes Markkanen Name of the doctoral dissertation Integral equation methods for extreme-parameter materials and novel boundary conditions Publisher School of Electrical Engineering Unit Department of Radio Science and Engineering Series Aalto University publication series DOCTORAL DISSERTATIONS 109/2013 Field of research El...

This paper studies a boundary value problem of nonlinear second-order q-difference equations with non-separated boundary conditions. As a first step, the given boundary value problem is converted to an equivalent integral operator equation by using the q-difference calculus. Then the existence and uniqueness of solutions of the problem is proved via the resulting integral operator equation by m...