Variational and Numerical Study for Eigenvalues Double-Phase Elliptic Problems with Robin Boundary Conditions

Numerical Study for Eigenvalues Double-Phase Elliptic Problems

Abstract

In this paper, we study the numerical approximation of the first eigenvalue in double-phase equation subject to Robin boundary conditions. When the parameters of this problem satisfy certain assumptions, particularly regarding the right-hand side function, we establish the existence of the first eigenvalue with its corresponding eigenfunction. The Physics-Informed Neural Networks approach is considered to approximate this solution. At the end, we conduct several numerical test for different exponents and analytical solution.