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The existence of positive solution to some asymptotically linear elliptic equations in exterior domains.

Gongbao Li, Gao-Feng Zheng (2006)

Revista Matemática Iberoamericana

In this paper, we are concerned with the asymptotically linear elliptic problem -Δu + λ0u = f(u), u ∈ H01(Ω) in an exterior domain Ω = RnO (N ≥ 3) with O a smooth bounded and star-shaped open set, and limt→+∞ f(t)/t = l, 0 < l < +∞. Using a precise deformation lemma and algebraic topology argument, we prove under our assumptions that the problem possesses at least one positive solution.

The p -Laplace eigenvalue problem as p → ∞ in a Finsler metric

M. Belloni, Bernhard Kawohl, P. Juutinen (2006)

Journal of the European Mathematical Society

We consider the p -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite p and investigate the limit problem as p → ∞ .

The Perturbed Generalized Tikhonov's Algorithm

Alexandre, P. (1999)

Serdica Mathematical Journal

We work on the research of a zero of a maximal monotone operator on a real Hilbert space. Following the recent progress made in the context of the proximal point algorithm devoted to this problem, we introduce simultaneously a variable metric and a kind of relaxation in the perturbed Tikhonov’s algorithm studied by P. Tossings. So, we are led to work in the context of the variational convergence theory.

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