Baker-Akhiezer modules on rational varieties.
Behaviour of the first eigenvalue of the p-Laplacian in a domain with a hole
We investigate the behaviour of a sequence , s = 1,2,..., of eigenvalues of the Dirichlet problem for the p-Laplacian in the domains , s = 1,2,..., obtained by removing from a given domain Ω a set whose diameter vanishes when s → ∞. We estimate the deviation of from the eigenvalue of the limit problem. For the derivation of our results we construct an appropriate asymptotic expansion for the sequence of solutions of the original eigenvalue problem.
Bifurcation for a semilinear elliptic equation on Rn with radially symmetric coefficients.
Bifurcation for nonlinear elliptic boundary value problems I.
This paper is devoted to local static bifurcation theory for a class of degenerate boundary value problems for nonlinear second-order elliptic differential operators. The purpose of this paper is twofold. The first purpose is to prove that the first eigenvalue of the linearized boundary value problem is simple and its associated eigenfunction is positive. The second purpose is to discuss the changes that occur in the structure of the solutions as a parameter varies near the first eigenvalue of the...
Bifurcation for some semilinear elliptic equations when the linearization has no eigenvalues
We prove existence and bifurcation results for a semilinear eigenvalue problem in , where the linearization — has no eigenvalues. In particular, we show...
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Bifurcation points and eigenvalues of inequalities of reaction-diffusion type.
Bifurcation theorems of Rabinowitz type for certain differential operators of the fourth order
This paper was inspired by the works of P. H. Rabinowitz. We study nonlinear eigenvalue problems for some fourth order elliptic partial differential equations with nonlinear perturbation of Rabinowitz type. We show the existence of an unbounded continuum of nontrivial positive solutions bifurcating from (μ₁,0), where μ₁ is the first eigenvalue of the linearization about 0 of the considered problem. We also prove the related theorem for bifurcation from infinity. The results obtained are similar...
Boundary eigencurve problems involving the biharmonic operator
The aim of this paper is to study the spectrum of the fourth order eigenvalue boundary value problem ⎧Δ²u = αu + βΔu in Ω, ⎨ ⎩u = Δu = 0 on ∂Ω. where (α,β) ∈ ℝ². We prove the existence of a first nontrivial curve of this spectrum and we give its variational characterization. Moreover we prove some properties of this curve, e.g., continuity, convexity, and asymptotic behavior. As an application, we study the non-resonance of solutions below...
Boundary eigencurve problems involving the -Laplacian operator.
Boundedness and monotonicity of principal eigenvalues for boundary value problems with indefinite weight functions.