Browsing by Author "Alexander, Byron Joseph"

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    Monotone and pseudomonotone operators with applications to variational problems
    (2015) Alexander, Byron Joseph; Ebobisse Bille, Francois
    This work is primarily concerned with investigating how monotone and pseudomonotone operators between Banach spaces are used to prove the existence of solutions to nonlinear elliptic boundary value problems. A well-known approach to solving nonlinear elliptic boundary value problems is to reformulate them as equations of the form A (u) = f, where A is a monotone or pseudomonotone operator from a Sobolev space to its dual. We seek to study the abstract theory which underpins this approach and proves the existence of a solution to the equation A (u) = f, implying the existence of a weak solution to the elliptic boundary value problem. Further, we examine properties of monotone and pseudomonotone operators, with an emphasis on a characterization, which involves the latter, and establishes a connection between the operator and the principal part of a partial differential equation. In addition, results relating monotone and pseudomonotone operators with variational inequalities are explored.