Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 14 1 2025 01 01 Some inequalities for eigenvalues of an elliptic differential operator 137 154 4429 10.22103/jmmr.2024.22939.1582 EN Shahroud Azami Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran. Mosayeb Zohrehvand Department of mathematics, Malayer University, Malayer, Iran Ghodratallah Fasihi-Ramandi Department of Pure Mathematics, Imam Khomeini International University, Qazvin, Iran. Journal Article 2024 02 12 ‎In the present paper, we investigate  the eigenvalues of an elliptic differential operator on compact Riemannian manifolds with boundary and derive a general inequality for these eigenvalues. Applying this inequality, we give universal estimates  for eigenvalues on compact domains of  complete submanifolds in an Euclidean space, and of complete manifolds admitting special functions. Finally, we find universal bounds on  the $(k+1)$-th eigenvalue on such objects in terms of the first $k$ eigenvalues independent of  the domains. https://jmmrc.uk.ac.ir/article_4429_1c26859bd15de6ed29681a0b82ff7f18.pdf