Asymptotic Behavior of Solution to Nonlinear Eigenvalue Problem

Asymptotic Behavior of Nonlinear Transmission Plate Problem

We study a nonlinear transmission problem for a plate which consists of thermoelastic and isothermal parts. The problem generates a dynamical system in a suitable Hilbert space. Main result is the proof of asymptotic smoothness of this dynamical system and existence of a compact global attractor in special cases.

A Nonlinear Eigenvalue Problem

My lectures at the Minicorsi di Analisi Matematica at Padova in June 2000 are written up in these notes1. They are an updated and extended version of my lectures [37] at Jyväskylä in October 1994. In particular, an account of the exciting recent development of the asymptotic case is included, which is called the ∞-eigenvalue problem. I wish to thank the University of Padova for financial suppor...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Asymptotic Shape of Solutions to Nonlinear Eigenvalue Problems

We consider the nonlinear eigenvalue problem −u′′(t) = f(λ, u(t)), u > 0, u(0) = u(1) = 0, where λ > 0 is a parameter. It is known that under some conditions on f(λ, u), the shape of the solutions associated with λ is almost ‘box’ when λ 1. The purpose of this paper is to study precisely the asymptotic shape of the solutions as λ → ∞ from a standpoint of L1-framework. To do this, we establish t...

Asymptotic Expansion of Solutions to Nonlinear Elliptic Eigenvalue Problems

We consider the nonlinear eigenvalue problem −∆u+ g(u) = λ sinu in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 2) is an appropriately smooth bounded domain and λ > 0 is a parameter. It is known that if λ 1, then the corresponding solution uλ is almost flat and almost equal to π inside Ω. We establish an asymptotic expansion of uλ(x) (x ∈ Ω) when λ 1, which is explicitly represented by g.