Related papers: Exact eigenvalues and eigenfunctinos for a one-dim…
In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on this quantities and their corresponding eigenfunctions.
We describe the spectrum of a non-self-adjoint elliptic system on a finite interval. Under certain conditions we find that the eigenvalues form a discrete set and converge asymptotically at infinity to one of several straight lines. The…
In this work we investigate the resolvent operator and completeness of eigenfunctions of a Sturm-Liouville problem with discontinuities at two points. The problem contains an eigenparameter in the one of boundary conditions. For…
This paper systematically studies the behavior of the leading eigenvectors for independent edge undirected random graphs generated from a general latent position model whose link function is possibly infinite rank and also possibly…
We consider the Dirichlet and Neumann eigenvalues of the Laplacian for a planar, simply connected domain. The eigenvalues admit a characterization in terms of a layer potential of the Helmholtz equation. Using the exterior conformal mapping…
This paper is concerned with continuous dependence of the n-th eigenvalue on self-adjoint discrete Sturm-Liouville problems. The n-th eigenvalue is considered as a function in the space of the problems. A necessary and sufficient condition…
In this paper we discuss spectral properties of operators associated with the least-squares finite element approximation of elliptic partial differential equations. The convergence of the discrete eigenvalues and eigenfunctions towards the…
This paper is concerned with the ergodic problem for viscous Hamilton-Jacobi equations having superlinear Hamiltonian, inward-pointing drift, and positive potential which vanishes at infinity. Assuming some radial symmetry of the drift and…
In this paper we describe the asymptotic behaviour of the spectral norm of the product of two finite Toeplitz matrices as the matrix dimension goes to the infinity. These Toeplitz matrices are generated by positive functions with…
In Gel'fand's inverse problem, one aims to determine the topology, differential structure and Riemannian metric of a compact manifold $M$ with boundary from the knowledge of the boundary $\partial M,$ the Neumann eigenvalues $\lambda_j$ and…
It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary…
This paper investigates the asymptotic behavior at infinity of ancient solutions to the Lagrangian mean curvature flow. Under conditions that admit Liouville type rigidity theorems, we prove that every classical solution converges at…
In this paper, we study the asymptotic behavior of positive solutions of the fractional Hardy-H\'enon equation $$ (-\Delta)^\sigma u = |x|^\alpha u^p ~~~~~~~~~~~ in ~~ B_1 \backslash \{0\} $$ with an isolated singularity at the origin,…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the…
It is shown that eigenvalues of Laplace-Beltrami operators on compact Riemannian manifolds can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polyharmonic functions with singularities. In…
In the present paper, we deal with a fourth-order boundary value problem problem with eigenparameter dependent boundary conditions and transmission conditions at a interior point. A self-adjoint linear operator A is defined in a suitable…
We find uniform asymptotic formulas for all the eigenvalues of certain 7-diagonal symmetric Toeplitz matrices of large dimension. The entries of the matrices are real and we consider the case where the real-valued generating function such…
Given a self-dual cuspidal automorphic representation for GL(2) over a number field, we establish the existence of an infinite number of Hecke eigenvalues that are greater than an explicit positive constant, and an infinite number of Hecke…
The aim of this work is to characterize the asymptotic behaviour of the first eigenfunction of the generalised p-Laplace operator with mixed (Dirichlet and Neumann) boundary conditions in cylindrical domains when the length of the…