In this paper, we discuss boundary value problems for a class of nonlinear elliptic equations with data on a boundary surface. We denote by y the unknown function which is supposed to take its values in  We assume that only some components of y are given on the whole boundary surface implying the designation of nonregular boundary value problems. To derive an interesting necessary condition for the solvability of our original problem, we construct an appropriate Cauchy problem for nonlinear elliptic equations which we solve by making use of a parameter ε which is small enough.

nonlinear PDE, Cauchy problem, elliptic operators.

Received: October 15, 2024; Revised: October 28, 2024; Accepted: November 18, 2024; Published: December 13, 2024

How to cite this article: I. Ly, T. Dabre and B. Bella, Nonregular boundary value problems with a parameter, International Journal of Numerical Methods and Applications 25(1) (2025), 41-61. https://doi.org/10.17654/0975045225002

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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