@article{Abdullayev_2024, title={The Neumann eigenvalue problem for the p(x) -Laplacian as p → ∞}, volume={14}, url={https://acta.polito.uz/index.php/journal/article/view/280}, abstractNote={<p>This paper is dedicated to the study of the behaviour of the second eigenvalues and the corresponding eigenfunctions for the p(x)-Laplacian subject to the Neumann boundary conditions in an open, bounded domain Ω ⊂ RN with smooth boundary. As p → ∞ one can obtain uniform bounds for the sequence of second eigenvalues and the positive second eigenfunctions. In the latter case, the uniform limit is a viscosity solution to a problem involving the ∞-Laplacian subject to appropriate boundary conditions.</p>}, number={1}, journal={Acta of Turin Polytechnic University in Tashkent}, author={Abdullayev, Farhod}, year={2024}, month={Mar.}, pages={18–26} }