Computation of topological degree in ordered Banach spaces with lattice structure and its application to superlinear differential equations

Using the cone theory and the lattice structure, we establish some methods of computation of the topological degree for the nonlinear operators which are not assumed to be cone mappings. As applications, the existence results of nontrivial solutions for superlinear Sturm–Liouville problems are given. We also investigate the singular superlinear Sturm–Liouville problems.