A LAPLACE–SERIES AND FIXED-POINT FRAMEWORK FOR A FAMILY OF NONLINEAR FREDHOLM INTEGRAL EQUATIONS WITH POWER-LAW NONLINEARITY
DOI:
https://doi.org/10.61841/9vg4mp30Keywords:
Nonlinear Fredholm integral equation, Laplace–series method, power-law nonlinearity, existence and uniqueness, bifurcation analysisAbstract
we focus on a family of nonlinear Fredholm integral equations (NFIE) of the second kind [2] with separable kernels and power-law nonlinearity. By combining Laplace transform techniques, power-series representations, and fixed-point theory, the integral equation is rigorously reduced to a finite-dimensional nonlinear algebraic equation. The solutions exist using Schauder’s fixed-point theorem, while local uniqueness is obtained via the Banach contraction principle. A complete parameter-dependent analysis is presented, identifying conditions under which solutions exist, are unique, or exhibit multiplicity. The results generalize known quadratic cases to arbitrary positive powers and provide a unified and transparent analytical framework.
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Mathwork,MATLAB Documentation (2023)
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