Αποτελέσματα Αναζήτησης
1 Ιαν 2012 · A nonlinear integral equation is an integral equation in which the unknown function appears in the equation in a nonlinear manner. The nonlinearity may occur either inside or outside of the integrand or simultaneously in both of these locations.
Nonlinear: An integral equation is nonlinear if the unknown function u (x) or any of its integrals appear nonlinear in the equation. [1] . Hence, examples of nonlinear equations would be the equation above if we replaced u (t) with , such as: Certain kinds of nonlinear integral equations have specific names. [3] .
When one or both limits of integration become infinite or when the kernel becomes infinite at one or more points within the range of integration, the integral equation is called singular. We shall mainly deal with functions which are either continuous or integrable or square integrable.
22 Μαΐ 2024 · An integral equation containing the unknown function non-linearly. Below the basic classes of non-linear integral equations that occur frequently in the study of various applied problems are quoted; their theory is, to a certain extent, fairly well developed.
We shall investigate nonlinear integral equations and their properties and solutions. Proofs and examples for the existence of unique solutions to nonlin-ear integral equations are provided. Some other areas explored are properties of solutions to systems of integral equations, integral inequalities, and multiple solutions to such equations.
Systems can be defined as nonlinear, regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives, even if nonlinear in terms of the other variables appearing in it.
A nonlinear integral equation is an equation in which an unknown function appears under an integral sign and is raised to a power or combined with itself in a non-linear way. These equations often arise in various fields such as physics and engineering, where they describe complex phenomena, including fluid dynamics and population dynamics.
