This subtopic studies linear integral equations, including Fredholm and Volterra-type problems and the operator-theoretic framework that unifies them.

This subtopic studies Fredholm integral equations, emphasizing solvability, spectral theory, and the structure of compact-operator formulations.

This subtopic studies eigenvalue problems for integral operators, including characteristic values, resolvents, and applications to spectral methods.

This subtopic studies Volterra integral equations, focusing on causal structure, existence and uniqueness, and triangular operator forms.

This subtopic studies singular integral equations, where kernels or operators have singular behavior requiring specialized analytical tools.

This subtopic studies systems of integral equations, emphasizing coupled operator equations and their solvability and spectral behavior.

This subtopic studies nonlinear integral equations, focusing on existence, uniqueness, iterative methods, and nonlinear operator phenomena.

This subtopic studies integro-ordinary differential equations, where differential equations are coupled with integral terms and memory effects.

This subtopic studies integro-partial differential equations, combining PDE structure with integral terms that model nonlocal interactions.

This subtopic studies random integral equations, where stochastic effects and probabilistic forcing influence integral-equation models.

This subtopic studies miscellaneous applications of integral equations, collecting special cases and cross-disciplinary uses not covered elsewhere.

This subtopic studies integral equations in abstract spaces, generalizing classical formulations to functional-analytic and operator-theoretic settings.

This subtopic studies numerical methods for integral equations, emphasizing discretization, stability, and computational approximation of solutions.

This subtopic studies special kinds of integral equations, including singular, degenerate, or otherwise structured cases requiring tailored analysis.