A mixed eigenvalue problem on domains tending to infinity in several directions

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Analysis shows eigenvalues depend on unbounded domains in one direction, suggesting new insights on elliptic operators and mixed boundary conditions.

Eigenvalues demonstrate distinct limiting behavior as domains expand infinitely in multiple directions, and the findings reveal new relationships with bounded cylindrical structures.
The asymmetric expansion of domains influences eigenvalue properties, significantly affecting the solutions of elliptic operators and their associated eigenfunctions.
Asymptotic behavior of the eigenfunctions was thoroughly discussed, indicating their relevance in the context of mixed boundary type conditions on cylindrical domains.
This analysis contributes valuable understanding to the field of partial differential equations, opening avenues for exploring further mixed eigenvalue problem scenarios.

Roy et al. (2025) studied this question.

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Analysis shows eigenvalues depend on unbounded domains in one direction, suggesting new insights on elliptic operators and mixed boundary conditions.