Eigencurves of the -Laplacian with weights and their asymptotic behavior.
Eigenfunctions and Nodal Sets
Eigenstructure of the equilateral triangle. II: The Neumann problem.
Eigenstructure of the equilateral triangle. III: The Robin problem.
Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with ) width ; ) and recover eigenvalue asymptotics with sharp remainder estimates.
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 distributions of some degenerate elliptic operators: an approach via entropy numbers.
Eigenvalue problems and bifurcation of nonhomogeneous semilinear elliptic equations in exterior strip domains.
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.
Eigenvalues and eigenfunctions of the Laplace operator on an equilateral triangle for the discrete case
A discretized boundary value problem for the Laplace equation with the Dirichlet and Neumann boundary conditions on an equilateral triangle with a triangular mesh is transformed into a problem of the same type on a rectangle. Explicit formulae for all eigenvalues and all eigenfunctions are given.
Eigenvalues of polyharmonic operators on variable domains
We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are...