Eigenvalue asymptotics for the Schrödinger operator with perturbed periodic potential.
Eigenvalue asymptotics of the even-dimensional exterior Landau-Neumann Hamiltonian.
Eigenvalue clusters of the Landau Hamiltonian in the exterior of a compact domain.
Eigenvalue Comparison Theorems and Its Geometric Applications.
Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds
Eigenvalue distribution of random operators and matrices
Eigenvalue distributions of some degenerate elliptic operators: an approach via entropy numbers.
Eigenvalue estimates for a class of operators related to self-similar measures
Eigenvalue estimates for the weighted laplacian on a riemannian manifold
Eigenvalue estimates on homogeneous manifolds.
Eigenvalue Inequalities for the Dirichlet Problem on Spheres and the Growth of Subharmonic Functions
Eigenvalue problems for a mixed-type equation with two singular coefficients.
Eigenvalue problems for a quasilinear elliptic equation on .
Eigenvalue problems for degenerate nonlinear elliptic equations in anisotropic media.
Eigenvalue problems for the -Laplacian with indefinite weights.
Eigenvalue problems of quasilinear elliptic systems on Rn.
In this paper we get the existence results of the nontrivial weak solution (λ,u) of the following eigenvalue problem of quasilinear elliptic systems-Dα (aαβ(x,u) Dβui) + 1/2 Dui aαβ(x,u)Dαuj Dβuj + h(x) ui = λ|u|p-2ui, for x ∈ Rn, 1 ≤ i ≤ N and u = (u1, u2, ..., uN) ∈ E = {v = (v1, v2, ..., vN) | vi ∈ H1(Rn), 1 ≤ i ≤ N},where aαβ(x,u) satisfy the natural growth conditions. It seems that this kind of problem has never been dealt with before.
Eigenvalue problems with indefinite weight
We consider the linear eigenvalue problem -Δu = λV(x)u, , and its nonlinear generalization , . The set Ω need not be bounded, in particular, is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues .
Eigenvalue questions on some quasilinear elliptic problems
Eigenvalue stability bounds via weighted Sobolov spaces.
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle
A boundary value problem for the Laplace equation with Dirichlet and Neumann boundary conditions on an equilateral triangle is transformed to a problem of the same type on a rectangle. This enables us to use, e.g., the cyclic reduction method for computing the numerical solution of the problem. By the same transformation, explicit formulae for all eigenvalues and all eigenfunctions of the corresponding operator are obtained.