Wenying Feng, Department of Computing & Information Systems, Trent University
Nonlinear Boundary Value Problems in Ordered Banach Spaces
In proving existence of positive solutions for nonlinear boundary value problems, properly construction of the cone that defines the order of the Banach space is essential. We will introduce a new type of order-cones that can be used to prove existence of fixed points for nonlinear and semilinear operators on order intervals. The abstract results unified previous work in studying existence of solutions for boundary value problems using the cone methods. When they are applied to concrete cases such as nonlinear algebraic systems, Dirichlet boundary value problems and fractional differential equations, new results can be naturally obtained. We will also briefly discuss other topological methods in studying existence and multiplicity of solutions for nonlinear and semilinear boundary value problems.